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"metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bottom, top = 0.1, 24\n", + "x_size, y_size = 200, 200\n", + "xgrid = np.linspace(bottom, top, x_size)\n", + "ygrid = np.linspace(bottom, top, x_size)\n", + "X, Y = np.meshgrid(xgrid, ygrid)\n", + "\n", + "Z = np.empty((x_size, y_size))\n", + "\n", + "for i in range(x_size):\n", + " for j in range(y_size):\n", + " Z[i, j] = sk(xgrid[i], ygrid[j])\n", + "Z = Z.T\n", + "\n", + "fig, ax = plt.subplots(figsize=(9.5, 7))\n", + "\n", + "cs1 = ax.contourf(X, Y, Z, alpha=0.65)\n", + "ctr1 = ax.contour(X, Y, Z, colors='black', alpha=0.5)\n", + "\n", + "#plt.clabel(ctr1, inline=1, fontsize=10)\n", + "plt.colorbar(cs1, ax=ax, format=\"%.4f\")\n", + "\n", + "ax.plot(xgrid, xgrid, 'k-', lw=2.0, alpha=1)\n", + "\n", + "#ax.grid(True)\n", + "ax.set_xlabel(r'$w$', fontsize=16)\n", + "ax.set_ylabel(r\"$w'$\", fontsize=16)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Time series" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "

" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n = 2000\n", + "w = np.empty(n)\n", + "w[0] = 0.0\n", + "\n", + "for t in range(n-1):\n", + " w[t+1] = (1 + r) * s(w[t]) + exp(mu + sigma * np.random.randn())\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(w, label=\"$w_t$\")\n", + "ax.set_xlabel(\"time\")\n", + "ax.set_ylabel(\"wealth\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Now with stochastic returns\n", + "\n", + "We'll compute the integral in the stochastic kernel by Monte Carlo" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "M = 5000\n", + "r_sigma = 1.0\n", + "r_mu = - r_sigma**2 / 2 # maintain unit mean\n", + "R_draws = (1 + r) * exp(r_mu + r_sigma * np.random.randn(M))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.hist(R_draws, bins=25, density=True)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.1015972372833205" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R_draws.mean()" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "@njit\n", + "def sk2(x, y):\n", + " return np.mean(phi(y - R_draws * s(x)))" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Z = np.empty((x_size, y_size))\n", + "\n", + "for i in range(x_size):\n", + " for j in range(y_size):\n", + " Z[i, j] = sk2(xgrid[i], ygrid[j])\n", + "Z = Z.T\n", + "\n", + "fig, ax = plt.subplots(figsize=(9.5, 7))\n", + "\n", + "cs1 = ax.contourf(X, Y, Z, alpha=0.65)\n", + "ctr1 = ax.contour(X, Y, Z, colors='black', alpha=0.5)\n", + "\n", + "#plt.clabel(ctr1, inline=1, fontsize=10)\n", + "plt.colorbar(cs1, ax=ax, format=\"%.4f\")\n", + "\n", + "ax.plot(xgrid, xgrid, 'k--', lw=1.5, alpha=1)\n", + "\n", + "#ax.grid(True)\n", + "ax.set_xlabel(r'$w$', fontsize=16)\n", + "ax.set_ylabel(r\"$w'$\", fontsize=16)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "@njit\n", + "def gen_wealth_ts(n=2000):\n", + "\n", + " w = np.empty(n)\n", + " w[0] = 0.0\n", + "\n", + " for t in range(n-1):\n", + " R = (1 + r) * exp(r_mu + r_sigma * np.random.randn())\n", + " w[t+1] = R * s(w[t]) + exp(mu + sigma * np.random.randn())\n", + " return w\n", + "\n", + "n = 2000\n", + "w = gen_wealth_ts(n)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(w, label=\"$w_t$\")\n", + "ax.set_xlabel(\"time\")\n", + "ax.set_ylabel(\"wealth\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Failure of Stability" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "α = 1.0\n", + "@njit\n", + "def q(x):\n", + " return 5.0 / (1 + exp(- α * (x - 10.0)))\n", + "\n", + "κ = 2.5\n", + "γ = 0.4\n", + "@njit\n", + "def g(x):\n", + " return κ + q(x) * x**γ\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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fPEfIt7gElRShmpU9LUh9eeVajgzD6HN20rVhGJHAZuDs6FEgsKw884iIiJS3tWvXMmTIEH777TeGDRvGQw89ZHWka3bsVG7JbbEM4g8V3x5LPZP/u+tqVPIoKUG+hJWMDPlXLf05QqWtPFerRQJTDMN4seShiaZpLjQM4/mS59BkbBERcWZvvvkmkyZNomHDhixbtozIyMgrf5HFTp7OO3dbLOFQ8cjQ8ay8313n6+NOaL2zt8WKR4bqVPNyyH2ZynNCdjTQ5BKPa/m+iIg4NdM0MQyD1q1bM2bMGN58800qV65sdazfOZNXyPZDmWxLyWBbciZxyRmXPHajipfb/+YIlRSh+tW9HbIIXYo2gRQRESkjmZmZTJgwgdq1a/PGG2/Qs2dPevbsaXUsAAqKbOw+lsW25Ey2JWewLSWD3ceysF209MnHw5WQutXOzREKq+9LQz8fXFycowhdisqRiIhIGfjhhx8YNWoUR44c4YUXXrA0y9mVY3EpGcVFKDmD7Yczf7eXkKuLQXCdKrQI8KVlfV9aBPhyc+3KuDpxEboUlSMREZFSlJqayrhx45gzZw4hISF88803tG7dunwznM5jW0oGcSWjQvEpGZc8eLVRDR9aBPjSoqQIBdetipe7a7lmtUcqRyIiIqXo8OHDfP3110yePJmXXnoJD4+y3a8nO7+Q7YdOsS0549zIUEr67+cJ1ajkQcuA4hLUIqB49Vj1ctpU0dGoHImIiNygo0ePsnDhQsaMGUNoaCgHDx4sk80cC4ts7D52umTCdAZxyZeeJ+Tt7kpo/WrFZai+Ly0CqlHP13kmTJc1lSMREZHrZJomc+bM4emnnyY7O5tevXrRuHHjUitGx0/lsuVgBluT09l6sHin6ZyCC4/acHUxCLqpZJ5QQLXieUK1KuPm6lIqGSoilSMREZHrkJKSwsiRI1myZAnt27fns88+o3Hjxtf9enmFRSQePsWWA+lsTc4g7uCll9E38Ds7T6h4ZCi4bjW8PTRPqDSpHImIiFyjgoICOnbsyIkTJ3jvvfcYPXo0rq5XX1BM0yQlPYetyRlsPVg8KrTj8Cnyiy5cPVbZ040WAdW4LaA64Q2Lb5HVsLOjNpyRypGIiMhVSk5Opl69eri7u/Ppp59yyy23EBgYeMWvy84vJD4lky0lRWjrwQxOnr5wl2nDgFv8K3NbQHVua+DLbQ2qV8hl9PZA5UhEROQKbDYbH374IS+++CLvvPMOo0aN4q677rrMtSb7Us+UlKDiMvTr0VO/mzTt6+PObQG+hDeozm0NqhMWUI2qXu7l8N3IlagciYiI/IFdu3YxdOhQ1q1bx913302vXr0ueD4zp4BtyRnnRoXikjN+dxq9q4tBSN0qF4wKNarho9VjdkrlSERE5DJmzZrFmDFj8PHx4f/+7/8YNGgQyek5LIpNIeZAOlsOpLP7eBbmRaNCtap4Et7gf6NCofU0adqRqByJiIhcRt2AANp368ndI15mTZYb7725nJOn8y+4xsPVheB6VUuKUPGoUF0HPY1eiqkciYiIlDiclsXzk17jSEY2vp0eISHFRn6LUXy0MfXcNTUqeRDesDoRDavTqmF1QupV05EbTkblSEREKiSbzWTPidPE7E8n9kA6K9euJ2Hu2xScPEClkO7UCEjDMAxu8a9Mq4bVadXQj1YNNVeoIlA5EhGRCiE7v5C45Axi96cTe7B4vtCp3EJsBXlkrvuKU5u+wa1ydTo9OZX777+P8IbVCQ+oTjUfrSCraFSORETEKZ3IyiNmfxqb9qcRsz+dHUdOUXTRevq61bxo5JrDgi3f82D/QUR9+C41a/hZlFjshcqRiIg4PNM0SU7LYdP+NDbvS2Pz/jSSTp654BpXF4PQetVo1bA6wbU9ORK3iqdGDQXgrf6tadiwoRXRxQ6pHImIiMOx2Ux2Hcti8/40NpWUoWOnLtxx2tvdlfCGvrRpVIPWjarTIsCXSp5uLF++nOEDh7N//366d2xLSEiIipFcQOVIRETsXn6hjYRDGWzal87m/WnE7E/jVG7hBddU93EnopEfbRr50bqxH8F1q+J+3sn0mZmZjHzqeaKiomjatCmrVq0iJCSkvL8VcQAqRyIiYney8wuJPZDOpn3FI0NxyRnkFV54KGs9X29aN6pO68bFhahJrcq4XOYcMpvNRqdOnUhMTOS5557jtddew9vbuzy+FXFAKkciImK5s2VoQ1IqG5LS2JacQeFFk6eb1q58rgi1buxHPd8rl5v09HSqVauGi4sLr7/+OnXr1qV169Zl9W2Ik1A5EhGRcnelMuRiQFj9arRt7EfrRn5ENPLDr5LHNb3HokWLePLJJ5k8eTJPPvkk999/f2l/G+KkVI5ERKTMXU0ZalG/GrcH1uD2wBq0alT9uk+oP3bsGGPGjGHhwoWEh4fToUOH0vo2pIJQORIRkVKXW1DE5v1pVxwZKi5DxSND11uGzvftt98yZMgQzpw5w1tvvcWECRNwc9M/dXJt9DdGRERuWJHNZPuhTNbuOcm6PSeJOZBO/nkTqMuqDF2scuXK3HrrrXz22Wfceuutpf76UjGoHImIyDUzTZN9J8+wbs9J1u45yfq9qRcsrTcMCKlXlXaBNWjXpEaZlSHTNPnss884evQokyZNokePHnTv3l1nn8kNUTkSEZGrcjwrl/V7U1n7W/Ho0OHM3Aueb+DnQ4eba9Lx5pq0a1LjmidQX6t9+/YxfPhwli9fTs+ePSkqKsLV1VXFSG6YypGIiFxSXmERMfvTWbX7BKt2nWDXsawLnver5EH7JjXoeHNNOtxckwA/n3LJZbPZ+Oijj3jhhRdwdXXl008/Zfjw4bi4uFz5i0WugsqRiIick5yWzcpdx1m1+wS/7E0lO7/o3HNe7i60aVyDjjfXoMPNNWl+U9XLbrpYlvbu3cv48ePp0aMHM2bMoEGDBuWeQZybypGISAWWW1DEhqTUc6NDFx/WeutNVejSrBZdmtaiVaPqeLq5WpKzsLCQJUuWcN9999G0aVNiY2MJCQnRLTQpEypHIiIVzNHMXKJ3HiN65zHW70294FiOKl5udGpak6631KbzLbW4qZqXhUmLJSQkMHjwYGJjY1m/fj233347oaGhVscSJ6ZyJCLi5EzT5NejWSzbUVyI4lMyL3g+pF5Vut5Smy7NanFbgC9urvYxdyc/P5+33nqLN954A19fX+bPn0/btm2tjiUVgMqRiIgTKiiysWlfGst2HGPZjmMcysg595yXuwudmtaiZ3N/ut1am1pVPC1MemmmaXLHHXewatUqBg4cyHvvvUfNmjWtjiUVhMqRiIiTyMkvYsWu4/y0/Sgrdx0n67x9h2pW9iSyeW0im/vTsWlNvNytmTt0Jbm5uXh4eODi4sKYMWMYP348vXv3tjqWVDAqRyIiDiwnv4iVu47zQ8IRft55nJyC/60ua1q7Mj2D/IkM8qdlfV9LVpZdi19++YUhQ4YwduxYRo8eTZ8+fayOJBWUypGIiIPJLShi5a4T/JhwhOU7j12w3L5lgC+9QuvQM8ifRjUrWZjy6p05c4aXX36Z999/nwYNGtCsWTOrI0kFp3IkIuIAbDaTDUmpLNySwtLtRzlzXiFqUb8avcLqcHdInXLbiLG0rF27lscee4ykpCRGjx7NW2+9RZUqVayOJRWcypGIiB1LOnGaRVtS+GbLoQuO6wirX41eoXW4J9TxCtH58vLycHNzY9WqVXTu3NnqOCKAypGIiN3JzC7g+/jDLNqSwtaDGecer+frzUPh9XgwvD6NHeSW2aUsWbKExMREnnvuOXr06EFiYiJubvrnSOyH/jaKiNgB0zTZvD+dLzce4KeEo+QXFW/MWMnDlXtC6/BQq/q0aeRn95Oq/0haWhrjxo3jiy++ICwsjKeffhoPDw8VI7E7+hspImKhzJwCvtmSwpcbD/Lb8dMAGAZ0alqTh8Lrc0ewPz4ejv+jetGiRYwePZrU1FT+8pe/8PLLL+Ph4WF1LJFLcvz/4kREHNBvx7KYvW4fi7cePrf8vlYVTx5uHUD/1gHUr+6484gulpyczMCBAwkODmbp0qW0aNHC6kgif0jlSESknJimybo9qcxck8Sq3SfOPd7h5hoMatuQnkH+uNvJ0R03yjRN1q5dS6dOnQgICODnn3+mTZs2uLu7Wx1N5IpUjkREylhBkY3FWw/x2dp9/Ho0Cyg+wqNPq/oM7tCYJrUqW5ywdB06dIhRo0bxww8/sHz5crp3706HDh2sjiVy1VSORETKSH6hjYWxKXy8cg8p6cVnm9Wq4slj7RoysG1D/Co515wb0zT57LPPGD9+PAUFBUyfPp0uXbpYHUvkmqkciYiUsrzCIubHpPDJij3n9iZqUqsSo7o04b6WdfF0s89zzW7Uww8/zPz58+natSszZ87k5ptvtjqSyHVRORIRKSWFRTYWxKbwXvRvHD1VXIpu8a/M2O5NuSe0Dq4OvAz/cmy24i0HXFxcePDBB+nWrRsjRozAxcU55k5JxaRyJCJyg0zTZPnO47z9n1/ZU7Ic/9abqvB0j6bcGXyTQ+9N9Ed2797N0KFD6d+/P2PGjOHhhx+2OpJIqVA5EhG5AduSM3hzyU427ksDoIGfD8/d2YxeoXWcthQVFhYyffp0XnnlFby8vBg1apTVkURKlcqRiMh1OJGVx5tLdvLN1kMA+Pq481T3pjxye0M83Jz3llJiYiKDBw9m8+bNPPDAA3z88cfUqVPH6lgipUrlSETkGthsJl9tOsiU//xKVm4hHm4uDOnQmCe6NqGat/Pv4XP8+HEOHDjAvHnz6Nu3L4bhnKNjUrGpHImIXKXEw5m8/M124pKLD4Pt2qwWf70vhAY1nGc360uJjY1l/fr1jBkzhm7durFv3z58fJz7e5aKTeVIROQKcguKmLZ0F7PX7cNmgn9VT17tHcxdITc59chJbm4uf/3rX5k6dSp16tTh8ccfp3LlyipG4vRUjkRE/sD2Q5mMmxfHnuOncTFgSIfGPHvHLVT2dO4fn+vXr2fIkCH8+uuvDBkyhGnTplG5snPt5C1yOc79X7eIyHUqspl8umov05ftptBmcnPtykzv15LQ+tWsjlbmTp48SY8ePahVqxZLly7ljjvusDqSSLlSORIRuUhyWjbPzo9j8/50AB5v34gX7r4VL3fn3Nn6rO3btxMSEkLNmjX55ptvaN++PVWqVLE6lki5c971piIi12FJwhHufm8Nm/enU7uKJ58PacOr9wU7dTE6deoUo0aNIjQ0lCVLlgBw5513qhhJhaWRIxERim+jTfvvLj5ZuReAu0Nu4s0HQ6nuZIfDXuynn35ixIgRHD58mPHjx9O1a1erI4lYTuVIRCq8jOx8xs7dyprfTuLqYvDyPc0Z3KGRU69EAxg3bhzvvfceQUFBLFy4kLZt21odScQuqByJSIW288gpRnwRQ3JaDn6VPPhoYDjtmtSwOlaZMk0TwzBo06YNkyZNYtKkSXh6elodS8RuqByJSIX1Y/wRJizYRk5BEaH1qvHpo62o5+ttdawyc/z4ccaOHUvHjh0ZO3YsAwcOtDqSiF3ShGwRqXBM02Tm6iRGf7WFnIIiHgqvz4JR7Zy2GJmmyVdffUVQUBCLFy+moKDA6kgidk0jRyJSoRTZTF7/YQf/+mU/AC/efSsjOgc67fyiQ4cO8cQTT/D999/Ttm1bZs+eTVBQkNWxROxauY4cGYYRaRjGsoseSzcMI9YwjCnlmUVEKp6CIhvj5sXxr1/24+HqwvsDbmNklyZOW4wAfvvtN5YvX84777zDunXrVIxErkK5jhyZphltGMbEix7ua5pmdHnmEJGKJ7egiDFfbSF653Eqe7oR9edWtG9S0+pYZWL//v38/PPPDBkyhK5du3LgwAFq1nTO71WkLNjDnCNfwzACrQ4hIs4rJ7+IIf/aTPTO4/j6uPPlsLZOWYxsNhsffvghISEhPPvss6SlpQGoGIlcI3soR35AmmEYMy71pGEYIwzDiDEMI+bEiRPlHE1EHF1OfhFDP9/ML3tTqVXFk3kj2tEiwNfqWKVu9+7ddO3a9dxqtG3btuHn52d1LBGHZPmEbNM0owAMw8gwDKOPaZoLL/F8FEBERISjAUfdAAAgAElEQVRpQUQRcVC5BUUM/7+Yc8Xo3yNup0kt5ztZPisr69wGjv/85z957LHHnHoelUhZs7QcGYYxAkgrKUSpVmYREeeSX2hj1JxY1u45Sc3Knswd7nzFKDk5mYCAAKpUqcJnn31Gu3btqFOnjtWxRBxeea9W6wNElPw/wHwgwzCMSICLR41ERK6HzWYyYcE2Vu46gV8lD+YOb8vNtZ2nGBUUFPD666/TpEkTvv32WwD+9Kc/qRiJlJLyXq22EFh43ucZwNmValqxJiI3zDRNJn+XyHfbDlPZ043PB7ehqb/znC6/detWBg8ezLZt23j44Ydp37691ZFEnI49TMgWESk1H63YwxcbDuDh5sLMP0cQWr+a1ZFKzdSpU2ndujXHjx9n8eLFzJ07l1q1alkdS8TpqByJiNP4Nu4Q0/67G8OA9x++zekOkK1Xrx5//vOfSUxM5P7777c6jojTMkzTcRaARUREmDExMVbHEBE7tGlfGo/M2kh+kY2/3BvE0I6NrY50w7Kzs5k0aRKNGzdm7NixVscRcXiGYcSaphlxpes0ciQiDu9gajYjvoghv8jGY+0aMqRDI6sj3bAVK1YQGhrK9OnTOXDggNVxRCoUlSMRcWhn8goZ8UUMGdkFdGtWi1d6Bzv0Hj+nTp3iiSeeoHv37hiGwcqVK5k2bZrVsUQqFJUjEXFYpmny3MJt/Ho0i8BalXhvwG24ujhuMQLYtm0bM2fOZPz48cTHx9OlSxerI4lUOJbvkC0icr0+XrmXJQlHqeLpxsw/R1DVy93qSNclLS2N6Oho+vXrR6dOndi7dy8NGza0OpZIhaWRIxFxSOv3pvLOf3cB8O7DLR129+vFixcTHBzMo48+yuHDhwFUjEQspnIkIg7neFYuT/17KzYTxnS7mR7N/a2OdM1OnDjBww8/zIMPPoi/vz8bNmygbt26VscSEXRbTUQcTJHN5Om5cZzIyuP2QD/GRTa1OtI1y83NJTw8nOPHj/O3v/2N559/Hnd3x7wlKOKMVI5ExKF8vGIP65NSqVnZk/cfvg03V8cZAE9LS8PPzw8vLy/efvttWrZsSXBwsNWxROQijvNTRUQqvK0H03l3+W8ATO/fgtpVvSxOdHVM02T27NkEBgayaNEiAAYNGqRiJGKnVI5ExCGczitk3Lw4imwmwzs1plNTxzhT7MCBA9x5550MHTqUFi1aEBYWZnUkEbkClSMRcQivfZfIgdRsmtepyoQ7m1kd56r861//IiQkhPXr1/Pxxx+zYsUKmjZ1vDlSIhWN5hyJiN2L3nGMBbEpeLq58P7DLfF0c7U60lXx8PCgffv2REVFaXm+iANRORIRu5aRnc+L3yQA8NydzWjqX8XiRJdXVFTEu+++i4+PD0888QQDBgxgwIABDn2ciUhFpNtqImLXXv0ukRNZebRuVJ3BHRpbHeeyEhMT6dChAxMmTGDNmjUAGIahYiTigFSORMRu/TfxKIvjDuPl7sLf+7Swy3PTCgoKeOONNwgPD2fPnj3MnTuXL7/80upYInIDVI5ExC6dyi3gL99uB+D5O2+lUc1KFie6tNjYWCZNmsSDDz7Ijh07ePjhhzVaJOLgVI5ExC5NW7qLY6fyaBngy2PtG1kd5wK5ubksWbIEgNtvv524uDj+/e9/U7t2bYuTiUhpUDkSEbsTeyCdLzYcwM3F4K0/hdrV7bQNGzYQHh5O79692bt3LwAtWrSwOJWIlCaVIxGxK/mFNl76OgHThBGdA2lep6rVkQDIzs5m/PjxtG/fntOnT7NkyRKaNGlidSwRKQNayi8iduWf6/ax61gWDWv48FQP+9gwsbCwkDZt2pCYmMgTTzzB22+/TdWq9lHaRKT0qRyJiN04mpnLeyVnp/31/hC83K3d7DEnJwdvb2/c3Nx45plnaNKkCV27drU0k4iUPd1WExG78caSnWTnF3FnsD9dbrH27LSlS5dy6623njsodujQoSpGIhWEypGI2IVf9p7k+23Fexr95d4gy3Kkp6czePBg7rrrLipVqkT9+vUtyyIi1lA5EhHLFRbZePW7RABGd72Z+tV9LMmxZMkSgoKC+OKLL3jppZfYsmULbdu2tSSLiFhHc45ExHLzY1LYfew0AX7eDO8caFmOjIwM/P39+fHHHwkPD7csh4hYSyNHImKpM3mF/GPZbgAm3nVruU7CNk2Tf//738ycOROAAQMGEBMTo2IkUsGpHImIpWasTuLk6eKdsHuF1im39z18+DAPPvggAwYM4KuvvsI0TQzDwM1NA+oiFZ3KkYhY5mhmLlGri3eZntSrebmcSWaaJv/85z8JCgpi6dKlTJs2jejoaJ2HJiLn6FckEbHMP5btIrfAxt0hNxHRyK9c3jM+Pp4hQ4bQuXNnZs2aRdOm9rHRpIjYj8uOHBmGUc0wjM2GYQwtz0AiUjHsPHKKBbEpuLkYTLzr1jJ9L5vNxrp164Dic9BWrVrFihUrVIxE5JIuW45M08wEooA7DcNINQzjLcMwtF++iJSKN5fsxDThkdsb0qhmpTJ7nz179tC9e3c6depEQkICAJ07d8bFRbMKROTS/vCng2maM03T7GeaZg1gPvCiCpKI3KhVu0+w5reTVPFyK7Pz04qKivjHP/5BWFgYcXFxzJo1i5CQkDJ5LxFxLlc958g0za3AVgDDMKqapnmqzFKJiNMqspm8tWQnAGO63YxfJY9Sfw+bzUZkZCQrV66kd+/efPrpp9StW7fU30dEnNM1jysbhvEpsO+8z28zDKNRKWYSESf2bdwhfj2aRT1fbx5r36hUX7uwsBAAFxcX+vbty1dffcW3336rYiQi1+R6brovA85tYVsyotTEMIzupZZKRJxSYZGN95b/BsAzPW8p1Q0f4+LiaN26NQsXLgTgySefZMCAAVqiLyLX7HrKURLQ9/y5R6ZpLgd8Sy2ViDilr7ce4kBqNo1rVuKBlqUzmpOXl8ekSZNo3bo1R48exdvbu1ReV0QqruvZ5ygS6A9MNQxjLxAN7AVaAV+XYjYRcSIFRTbeLxk1erpHU9xcb3y12KZNmxg8eDA7duzgscce4x//+Ad+fuWzX5KIOK/rKUdJpmlGQPF8I4qL0iigT2kGExHnsiAmhZT0HG6uXZneLUpn1CgpKYmsrCyWLFnC3XffXSqvKSJyPeXo3K9lF61g6w7sL51YIuJM8gqL+PDn4lGjcZFNcXW5/nlAq1evZv/+/fz5z3+mf//+9O7dm0qVym6fJBGpeK55XNs0zZmGYTxkGEbLs48ZhjEP0DHWInJJ8zcnczgzl2b+Vbgn5PoOl83KymL06NF06dKFv//97xQWFmIYhoqRiJS667rpb5rmItM04857aD4lI0giIufLLSjiwxV7AHimZ1NcrmPU6L///S8hISF88sknPPPMM2zYsAE3Nx0NKSJlo1R+upimuag0XkdEnM9XGw9y7FQeQXWqckfQTdf89b/99ht33XUXzZo1Y926dbRr164MUoqI/I8OFxKRMpOTX8THK/cC8GzPW65p1CgxMRGApk2bsnjxYrZu3apiJCLlQuVIRMrMlxsPcPJ0HmH1q9Gjee2r+poTJ04wYMAAQkND2bx5MwD33XcfXl5eZRlVROQc3bQXkTKRW1BE1OokoHiF2pV2qjZNk/nz5zNmzBgyMzN57bXXaNGiRXlEFRG5gMqRiJSJRVtSOJ6VR/M6VenW7I9HjUzTZNCgQcydO5fWrVsze/ZsQkJCyimpiMiFVI5EpNQVFtn4dFXxXKPR3ZpcdtTINE0ADMPg9ttvJzw8nHHjxmklmohYSnOORKTU/RB/hOS0HBrXrMTdl9nX6ODBg9x9993nDop96qmnmDBhgoqRiFhO5UhESpXNZvLxyuJ9jUZ1Cfzdbtg2m41PP/2U4OBg1q5dy5kzZ6yIKSJyWfoVTURKVfTOY+w+dpo61bx48Lb6Fzy3Z88ehg0bxqpVq4iMjGTmzJk0atTImqAiIpehciQipcY0TT4q2ddoeKdAPNwuHJyOjY1l69atzJo1iyFDhlxxBZuIiBVUjkSk1Kzfm8q25Az8KnnwcJsAAHbu3El8fDz9+/enX79+9OjRg5o1a1qcVETk8jTnSERKzUclc42GdGiEu2Hy5ptv0rJlSyZMmEBeXh6GYagYiYjd08iRiJSKrQfTWbcnlcqebrTwyaBt27Zs3bqVfv368cEHH+Dp6Wl1RBGRq6JyJCKl4uwZar1v9iKyS0eqV6/OokWL+NOf/mRxMhGRa6NyJCI3bO+J0/y0YTs+fv4880BbQl3/yV133YWfn5/V0URErpnmHInIDcnOzmbgsDEcmjGMtj4nqF3Fi4EDB6oYiYjDUjkSkeu2evVqQsLC2PTd51QO68mz/SOtjiQicsNUjkTkujz33HN06dKFzDN51H74Dfo9/Vdua1LX6lgiIjdMc45E5LrUqVOH0WOfYk21HmQWuDK8c6DVkURESoVGjkTkqmRkZDB06FDmz58PwLPPPku7Qc+SWeBKaL1qtG2sOUYi4hw0ciQiV/Tdd98xatQojh8/zi233AIUHzA7a80+AIZ3DtRRICLiNMp15MgwjEjDMJZd9FifksefL88sInJlJ0+eZNCgQdx///3UqlWLTZs2MXHiRKD4gNl9J89Qz9ebe0JusjipiEjpKddyZJpm9PmfG4bR57zHMwzD0FIXETuycuVKFixYwGuvvcbmzZsJDw8/99zZUaMhHRvj5qo79CLiPKy+rdYamFfycRIQDlxcoEYAIwAaNGhQruFEKqIjR46wefNm7rvvPh566CF2795No0aNLrhm68F0Nu1Po4qXG/1bB1gTVESkjFj9657vRZ/XuPgC0zSjTNOMME0zolatWuUUS6TiMU2Tzz//nKCgIB5//HFOnz6NYRi/K0bwv1GjgW0bUNnT6t+xRERKl9XlKAPQEhcRix08eJB77rmHxx9/nODgYNavX0/lypUveW1yWjY/bT+Cm4vB4PaNyzmpiEjZs/pXvs38b/QoEFj2B9eKSBlITU0lLCyMwsJCPvjgA5588klcXC7/e9Nna/dhM+GBlnW5qZpXOSYVESkf5b1arQ8Qcd5E7IVA4NmJ2BdP2BaRspOeng5AjRo1mDJlCgkJCYwZM+YPi1FmdgHzY5IBGNZJmz6KiHMq79VqC03TrF5Sis4+NtU0zWjTNKPKM4tIRVVUVMT06dMJCAhg7dq1AIwcOZLGja98i+zLTQfIzi+iU9OaBNWtWtZRRUQsYfVtNREpRzt37mTIkCFs2LCBe++995KTrS8nv9DGv9btBzRqJCLOzeoJ2SJSTqZPn07Lli3ZvXs3c+bM4bvvvqN+/fpX/fXfbTvM8aw8mvlXoXPTmmWYVETEWho5EqkgTNPkvvvu48MPP8Tf3/+av3bm6iRAR4WIiPPTyJGIk8rLy+OVV15hwYIFADzzzDMsWLDgmosRwOrfTrLrWBa1q3hyX4u6pR1VRMSuqByJOKFNmzbRqlUrXn/9ddatWwdwQ6M9s9YUjxo93qERHm76sSEizk0/5UScSE5ODs899xzt2rUjIyODH374gXffffeGXnPH4VOs+e0kPh6uDGrTsJSSiojYL5UjESeybNkypk2bxtChQ0lMTKRXr143/JpnR436RQRQzcf9hl9PRMTeaUK2iIM7ffo0GzdupEePHvTu3Zu4uDhatGhRKq99JDOH77YdxsWAoR11VIiIVAwaORJxYNHR0YSEhHDfffeRmpqKYRilVowA/vXLfgptJneH1iHAz6fUXldExJ6pHIk4oIyMDIYNG0bPnj3x8vJi2bJl1KhRo1Tf43ReIV9tPAjAcG36KCIViG6riTiY06dPExYWxuHDh3nhhReYPHkyXl6lfwDsvM3JZOUW0qaRHy0DfK/8BSIiTkLlSMRB5OTk4O3tTeXKlXn22Wfp2LEjERERZfJehUU2Zq/dBxRv+igiUpHotpqInTNNkwULFtC4cWPWrFkDwLhx48qsGAEs2X6UQxk5BNasRI9ba5fZ+4iI2COVIxE7dvToUR566CH69etH/fr1qV69epm/p2ma55bvD+3UGBcXHRUiIhWLypGInfrqq68ICgpiyZIlTJkyhQ0bNhASElLm77shKY34lEz8KnnwUPjVH0wrIuIsNOdIxE4dO3aM5s2bM3v2bJo1a1Zu7ztj9V4AHmvXCC9313J7XxERe6GRIxE7YbPZmDFjBosWLQLgqaeeYvXq1eVajH49eoqVu07g5e7Co+10VIiIVEwqRyJ2YO/evURGRjJq1CgWLFgAgKurK66u5TtyE7W6eK5R/4gA/Cp5lOt7i4jYC5UjEQsVFRXx3nvvERYWRmxsLFFRUcydO9eSLEcyc/gurviokGHa9FFEKjDNORKx0PLlyxk3bhy9evXi008/pX596yZAz167j0Kbyb1hOipERCo2jRyJlLPCwkI2btwIwB133MGKFSv4/vvvLS1GmTkFzN2UDMDIzk0syyEiYg9UjkTKUXx8PLfffjtdunQhJSUFgK5du2IY1u4l9NXGg5zOK6R9kxqE1q9maRYREaupHImUg/z8fCZPnkyrVq1ITk5mzpw5lo4UnS+vsIh/ris+KmRkF40aiYhozpFIGcvLy6NNmzbEx8fzyCOP8O6771KjRg2rY53z7dbDHM/K49abqtC5aU2r44iIWE4jRyJlpKioCABPT0/69+/P999/zxdffGFXxchmM89t+jiyS6Dlt/dEROyBypFIGVi7di3BwcGsXr0agJdeeol7773X4lS/t/zX4+w9cYa61by4N6yu1XFEROyCypFIKTp9+jRjx46lc+fO5OXl2fVIjGmafLRiDwBDOwXi7qofByIioHIkUmqWL19OaGgoH330EWPHjiUhIYFOnTpZHeuy1u1JJS45A79KHgxoE2B1HBERu6EJ2SKlJD4+Hg8PD1avXk3Hjh2tjnNFH674DYChHRvj46EfBSIiZ2nkSOQG/PDDDyxevBgoPig2Li7OIYpRzP40NiSlUcXLTQfMiohcROVI5DqkpqbyyCOP0Lt3b9577z1M08TV1RVvb2+ro12VD0vmGg1u34iqXu4WpxERsS8qRyLXaOHChQQFBTFv3jwmT57M0qVL7Xri9cUSUjJZuesEPh6uDO7Q2Oo4IiJ2RxMNRK7BL7/8Qt++fQkPD2fZsmWEhYVZHemanV2h9sjtDaleycPiNCIi9kcjRyJXYJomO3bsAKB9+/YsXLiQjRs3OmQx2n0si/8kHsXDzYVhnTRqJCJyKSpHIn8gOTmZe++9l/DwcPbuLd5J+qGHHsLNzTEHXT8uGTV6uHUAtat4WZxGRMQ+qRyJXIJpmkRFRREcHMzKlSuZOnUqjRo1sjrWDdl/8gzfbTuMm4uhA2ZFRP6AY/76K1KGioqKuPvuu1m2bBndu3dn5syZBAYGWh3rhn2yci82E/q0qkc9X8dYVSciYgWVI5ESpmliGAaurq60a9eOvn37MmzYMIdaiXY5+06eYeGWFFxdDJ7serPVcURE7Jpuq4kAu3btonPnzucOin3ttdcYPny4UxQjgOnLdlNkM+nbqj6NalayOo6IiF1TOZIKrbCwkClTptCiRQsSExNJS0uzOlKp23nkFN/HH8bD1YWxPZpaHUdExO7ptppUWPHx8QwZMoTY2FgefPBBPv74Y2666SarY5W6d/67G9OEgW0baK6RiMhVUDmSCmvFihUcPHiQ+fPn06dPH6e5hXa+rQfTid55DG93V0Z301wjEZGrodtqUqHExMTw448/AjBmzBh27txJ3759nbIYAUz77y4ABndoRK0qnhanERFxDCpHUiHk5OQwceJE2rZty0svvYTNZsPV1ZUaNWpYHa3M/LLnJOv2pFLFy42RnbWvkYjI1VI5Eqe3bt06WrZsydSpUxk6dCirV6/GxcW5/+qbpsnfS0aNRnQKpJqPu8WJREQch+YciVOLj4+nU6dONGzYkGXLlhEZGWl1pHLx86/H2XowgxqVPBjcUWeoiYhcC+f+9VkqrJSUFADCwsKYNWsWCQkJFaYY2Wwm0/67G4Anujahsqd+BxIRuRYqR+JUMjMzGTFiBE2bNuXXX38FYMiQIVSuXNniZOXn662H2HnkFDdV9eKR2xtaHUdExOHoV0pxGj/++CMjR47kyJEjjB8/noYNK14xyM4vZNrS4rlGz93ZDC93V4sTiYg4HpUjcXimaTJ48GA+//xzgoOD+eabb2jdurXVsSwxc/U+jp7KJaReVR68rZ7VcUREHJJuq4nDMwyDOnXq8MorrxAbG1thi9HxU7nMWL0XgEm9gnBxcc69m0REyppGjsQhHTt2jDFjxjB69Gi6du3KW2+9ZXUky/196S6y84u4I8if2wOdd/8mEZGyppEjcSimaTJnzhyCgoL4/vvv2bNnj9WR7MLWg+ksiE3B3dXgxXuaWx1HRMShqRyJw0hJSaF37948+uijNGvWjLi4OIYNG2Z1LMsV2Uxe+TYRgOGdAmlcs5LFiUREHJvKkTiMxYsXs2LFCt59913WrFnDrbfeanUkuzA/JpmEQ5ncVNVLh8uKiJQCzTkSu7Zv3z727t1LZGQkTz75JL17966QS/QvJyM7n6n/Kd7P6eVezamkDR9FRG6YRo7ELtlsNj744ANCQkIYPnw4hYWFuLi4qBhd5O2ffiU9u4DbA/24N6yO1XFERJyCypHYnV27dtG5c2eeeuopunTpwurVq3Fz04jIxTYkpfLvzcl4uLrwtwdCMAwt3RcRKQ36F0fsSlJSEi1atMDHx4fPP/+cRx99VP/oX0JeYREvfZMAwJPdmnBz7SoWJxIRcR4qR2IX0tPTqV69OoGBgbz99tv079+fOnV0m+hyPl6xl6QTZ2hSqxJPdG1idRwREaei22piqfz8fF577TUaNGjAzp07ARg3bpyK0R/YeeQUH68s3t/prT+F4emm89NEREqTRo7EMjExMQwZMoSEhAQGDRpErVq1rI5k9/ILbTw7fxsFRSaP3N6ANo39rI4kIuJ0NHIklnj55Zdp27YtqampfPfdd8yZM4eaNWtaHcvuffjzb+w8cooGfj68eLd2whYRKQsqR2KJ/Px8Bg8eTGJiIr1797Y6jkOIT8ngo5V7MQz4e58w7WkkIlJGLP/pahhGOpAERJumOdHqPFI2zpw5w0svvcSDDz5I165dmTp1qlahXYMzeYWM+3ccRTaTIR0a01YHy4qIlBnLyxHQ1zTNaKtDSNlZvnw5w4cPZ9++ffj7+9O1a1cVo2v06neJJJ08wy3+lXn+rmZWxxERcWr2cFvN1zCMQKtDSOnLzMxk5MiRREZG4urqyqpVq3jppZesjuVwvtt2mAWxKXi6ufDhwHC83LU6TUSkLNlDOfID0gzDmHGpJw3DGGEYRoxhGDEnTpwo52hyI+bNm8esWbOYMGEC27Zto3PnzlZHcjgHUs/w8tfFmz2+0juIW/y12aOISFkzTNO0OgMAhmFMATabprnwctdERESYMTEx5ZhKrlVaWho7duygY8eO2Gw2tm/fTlhYmNWxHFJOfhEPfryOX49mcVfwTXzySLhuR4qI3ADDMGJN04y40nWWjhyVjAr1Kfk01coscuMWLVpEUFAQffr0ITc3FxcXFxWj62SaJi9+Hc+vR7MIrFmJqX3DVIxERMqJ1bfV5gMZhmFEAvzRqJHYr2PHjtG3b1/69OlD3bp1Wbp0KV5eXlbHcmif/7KfxXGH8fFw5dNHW1HVy93qSCIiFYalq9VM08wAzq5U04o1B3TkyBFCQ0PJysrizTffZMKECbi76x/yG7F69wle/7H4KJWpfcI0z0hEpJzZw1J+cUC5ubl4eXlRp04dnn76afr06UPz5tqx+UbtPpbF6C+3UGQzeaJrE+4Nq2t1JBGRCsfq22riYEzTZNasWTRs2JAdO3YA8Je//EXFqBScyMpj8D83k5VXyD2hN/HcHdrPSETECipHctX27dvHHXfcwfDhwwkKCsLb29vqSE4jK7eAwf/axKGMHFoE+PKPfi1xcdEEbBERK6gcyVX55JNPCA0NZePGjXzyyScsX76cxo0bWx3LKeQWFDHs8xi2HzpFwxo+zPpzhDZ6FBGxkOYcyVXZt28fHTt2JCoqigYNGlgdx2kUFNkY89UWNu5Lw7+qJ3OGtqVWFU+rY4mIVGgqR3JJhYWFTJ8+nYiICLp168Ybb7yBm5ub9topRfmFNkZ/tYXoncfx9XHni6FtCfDzsTqWiEiFp9tq8jsJCQm0a9eO559/nsWLFwPg7u6uYlSK8gqLeGJOLMt2HKOatztfDGmrJfsiInZC5UjOyc/P569//SutWrXiwIEDzJs3j3fffdfqWE7nTF4hwz6PYfmvxSNGXw5rS2j9albHEhGRErqtJufMmzePyZMnM2DAAN577z1q1apldSSnc/J0HkP+tZn4lEz8KnkwZ2hbgupWtTqWiIicR+WogsvNzSUxMZFWrVoxaNAgAgIC6Nq1q9WxnNL+k2d4/J+b2J+aTYCfN58PbkNgrcpWxxIRkYvotloF9ssvv9CyZUvuuOMOTp06hYuLi4pRGVnz2wnu/2gd+1OzCa5blUVPtFcxEhGxUypHFdCZM2cYN24cHTt2JCcnh7lz51K1qm7tlAXTNJm1JonHZm8iM6eAyOa1mTeyHbWr6GBeERF7pdtqFUx6ejoREREkJSXx5JNP8vbbb1OlilZJlYWM7HyeXxjPf3ccA+Cp7jczLvIW7XwtImLnVI4qiKKiIlxdXalevTp9+vThnnvuoUuXLlbHclqb96cx7t9xHMrIoYqnG1P7hHF3aB2rY4mIyFXQbbUK4KeffqJZs2YkJiYCMGXKFBWjMpKTX8TffthBvxnrz52TtuTpTipGIiIOROXIiaWlpfHYY49xzz334OnpSUFBgdWRnNove09yz/trmLV2Hy6GwehuTVg4qs44+gwAAA1vSURBVJ12vRYRcTC6reakFi9ezKhRo0hNTWXSpElMmjQJT0+d2VUWjmbm8rcfd/BD/BEAbvGvzLS+LQir72txMhERuR4qR05q/fr11K1bl//85z+0bNnS6jhOKSu3gKjVScxas4+cgiK83F0Y0+1mhncOxNPN1ep4IiJynQzTNK3OcNUiIiLMmJgYq2PYJdM0mTt3LnXr1qVr167k5eXh4uKCu7u71dGczpm8Qr7aeJBPVu0l7Uw+AHcF38Ske5tTv7puoYmI2CvDMGL/v717jY2qzOM4/ntmehlagUIptZgIVnYppdEUBxDcCNVuIgkJ2FStL9y4pqI1LC9aoiQbzK5ijETUmICCpuKakOxquEjcmIARs/ESysUFrFCgWt1WpEJLsWWYdubZF52WQwVKb5w57feTTM61M//y5El/nPPMeay1wd7O48rRMFBfX6+ysjLt2LFDJSUlWrBgAbfQhkBzW1jvfVmnys+/U1Nb5/itWVPGaeXCHN0xebzL1QEABgvhyMOstaqsrFRFRYXC4bBeeeUVLV++3O2yhp1vf2rRP778XlsP1CvUHpUk5d+cpr/cM1UF0ybKGJ5bBADDCeHIw7Zt26bS0lLNnz9fb7/9tqZOnep2ScPGqXMhffh1g7bsr1f1Ty3d++/+fYaevDtbc29NJxQBwDBFOPKYaDSqmpoa5eTkaPHixXr//fdVVFQkn4+nMgzU2fPt2n30lLbsr9d/jjUqGhuONyaQoCX5N+lPc6do6kTmQwOA4Y5w5CE1NTUqLS3VoUOHdOzYMU2YMEHFxcVul+VZ1lod/fmcPj3SqE+PntK+uiZFYoko0W9077SJKsq/SQU5ExVI5NtnADBSEI48oKOjQ6+++qqeffZZBQIBvfbaa0pPT3e7LM+JRq2OnfpV++qatK+uSV+e+EUNZ0Pdx/0+o9m3jNei27K06LZJGp+a5GK1AAC3EI7iXGtrq+655x7t2bNHixcv1htvvKGsLKai6E00avVjU5u+/emcvv2pRV//2Kz9PzTpXKjjkvMm3JCsBdMyVDBtov7wuwkaO4pHHwDASEc4ilPWWhljlJqaqjlz5qi8vFwPPvggg4B7OB+O6Iczbfr+dKvqTrfqu19adeTkOR09eU5t4chvzp80NqCZk8cpOHmcglPGKzdrjHw+/k0BABcRjuLQ/v37VVZWpsrKSs2YMUOvv/662yVdd9ZatYUjOtkS0s+x18mzFy6ut4TU0HxeP7dcuOJ7TBydrOlZY5STNVozJo1VcPI4TUobdR1/CwCAFxGO4kgoFNJzzz2nNWvWKCMjQ6dOndKMGTPcLqvPolGr8+0RtYY71Hahc3k+HFFrOKK2Cx2dy3CHfr3QobNt7Wpua1dTW1jN59t11rEe7oj2+lkJPqObx6docnqKJqenanJ6iqZljta0G0cr/QYehAkA6DvPhaMTjb/q9K9hdU170jX5SdcsKFbdK1c9bnsc79x36XvqSj/zm/e+fC26wmddrpYj/92r1/9Wof99d1z3Ln5Ify5fpZYxadr+df3V63e8dzRqFbFWkahVNLa8uK7L7Os8Pxrtcbx7n1V7JKpwJKpwR1QXOjqXzn3dr4hVuCOicCTa/aDEgUpO8ClzTEA3jgkoc2xAmaOTdePYgCbG9mWN7Xwl+HmMAQBg8HguHK379Li27K93u4xB17T7PbWePquJD/xdx7Pv0F///b3bJQ3IqES/UpP9SklKUEqSX6nJsWVSglKSLy7TRiUpLSVRaaMSlZYSW09JVNqoJI1K4uvzAIDrz3PhKHtCqmZNGSdJMooNpL10IdO9bS7dvsJ+p64Bz799r6sfV8/PuoZa6qv3yufza1LOTHXklCsaWa7kUamXfE5favH5jPzGdC59urhujPw+c+lx03nOJcd7nOf3SYl+n5ISfErquUy4uJ3o9yk5tp3o9ymQ6JefQc4AAI8y1trez4oTwWDQ7t271+0yBqylpUXPPPOM3nzzTRUWFmrnzp1ulwQAwLBnjNlnrQ32dh6DNa6zjz/+WHl5edq4caMqKiq0fft2t0sCAAAOnrut5mWffPKJFi5cqOnTp+vzzz/XnXfe6XZJAACgB64cXQf19Z0DyAsKCrRhwwYdOHCAYAQAQJwiHA2hxsZGlZSUKC8vTydPnpTP59PSpUuVnMzzdwAAiFeEoyFgrdXmzZs1ffp0bd26VStWrGCiWAAAPIIxR4MsHA6ruLhYO3bs0OzZs7unAAEAAN7AlaNBlpSUpMzMTL388sv64osvCEYAAHgM4WgQ1NXVadGiRTp8+LAk6a233lJFRYX8fp7wDACA1xCOBiAajWrdunXKy8vTZ599ppqaGrdLAgAAA0Q46qdjx45pwYIFWrZsmebNm6fDhw+rqKjI7bIAAMAAMSC7n959910dPHhQlZWVevTRRy+ZCw0AAHgXc6v1wTfffKOWlhbNnTtXoVBIZ86c0aRJk1yrBwAAXDvmVhtE7e3tWr16tfLz87V8+XJZaxUIBAhGAAAMQ4SjXhw4cECzZs3SqlWrVFRUpI8++ohbaAAADGOMObqKPXv2aN68ecrIyNDWrVu1ZMkSt0sCAABDjCtHl9Hc3CxJCgaDWr16taqrqwlGAACMEIQjh7a2NpWXl+vWW29VQ0ODfD6fVq5cqXHjxrldGgAAuE64rRaze/dulZaW6sSJEyorK9Po0aPdLgkAALhgxF85ikQieuqpp1RQUCCpMyStX7+ecAQAwAg14sOR3+9Xa2urysvLdfDgQc2fP9/tkgAAgItGZDhqampSaWmpDh06JEnatGmT1q5dq5SUFJcrAwAAbhtx4Wjbtm3Kzc3Vpk2b9NVXX0kSzy0CAADdRkw4amxsVElJie6//35lZmaqqqpKjz/+uNtlAQCAODNiwtH69eu1ZcsWPf/886qqqlJ+fr7bJQEAgDg0rCeebWhoUENDg4LBoEKhkGpra5WbmzuEFQIAgHg1oieetdbqnXfeUW5urh555BFFo1EFAgGCEQAA6NWwC0d1dXW677779Nhjj+n222/Xhx9+KJ9v2P2aAABgiAyrJ2RXV1drzpw5stZq3bp1evLJJwlGAACgT4ZFOAqFQgoEAsrJydGyZcv0xBNPaMqUKW6XBQAAPMjTl1UikYjWrl2r7Ozs7oliX3zxRYIRAADoN8+Go+rqat11111asWKFgsEgD3IEAACDwvVwZIwpNsYUGmOevpbzrbV64YUXlJ+fr+PHj2vz5s3avn27srKyhrpUAAAwArgajowxxZJkrd0lqdkYU3gNP6MjR45oyZIlqq6u1sMPP8xVIwAAMGjcHpA9S9I/Y+u1kmZK2tXbD1VWVioxMXEo6wIAACOU27fV0npsp/c8wRiz1Biz1xizt7GxUZIIRgAAYMi4HY6aJY2/2gnW2o3W2qC1NpiRkXGdygIAACOV2+GoShevHmVL2uliLQAAAO6GI2vtB5KyuwZixwZmAwAAuMbtAdmy1q5xuwYAAIAubt9WAwAAiCuEIwAAAAfCEQAAgAPhCAAAwIFwBAAA4EA4AgAAcCAcAQAAOBCOAAAAHAhHAAAADoQjAAAAB8IRAACAg7HWul3DNTPGnJN01O060C8TJP3idhHoM9rNm2g376LthtZka21Gbye5PvFsHx211gbdLgJ9Z4zZS9t5D+3mTbSbd9F28YHbagAAAA6EIwAAAAevhaONbheAfqPtvIl28ybazbtouzjgqQHZAAAAQ81rV44AAACGFOEIAADAwTPhyBhTbIwpNMY87XYtuHbGmCZjzD5jzEtu14LexfrYzh776Htx7grtRt+Lc8aYtFj/Kna2E33OfZ4IR8aYYkmy1u6S1GyMKXS5JFy7B6y1d1hrn3G7EPQu1se60fe8oWe7xdD34t+DksZbaz+QJGPMUvpcfPBEOJI0S1JtbL1W0kwXa0HfpBljst0uAv1G3/Mu+l6cs9ZutNZ2fTstW9Iu0efiglfCUVqP7XRXqkB/jJd0xhizwe1C0C/0Pe+i73lELMSesdbWij4XF7wSjprV2dHhMbH/GTWr8/Jwsdv1oM/oex5F3/OUYmvtE7F1+lwc8Eo4qtLFNJ0taedVzkWccN4/l3Ta1WLQX/Q9D6LveYcxpthauya2Xij6XFzwRDiKDVbL7hqYdoXBh4g//5JjQGHXoEPEr9gf1KBjUCh9zwN6tpvoe54Qa5+XYt8q3CfR5+IFT8gGAABw8MSVIwAAgOuFcAQAAOBAOAIAAHAgHAEAADgQjgAAABwIRwAAAA6EIwAAAAfCEQAAgAPhCAAAwIFwBAAA4JDgdgEAMFDGmKWSzqhzos5dseUfHTOdA8A1Y241AJ4Wm9X8g9j6Pkkb1Dnx6neSbrHWNrtZHwDvIRwB8DRjzExr7f7YepMIRAAGiDFHADzNEYxmSqolGAEYKMIRgOHiIXWON5LUHZYAoM8IRwA8yxhTbIx5P7ZZKOlEbH+hJK4gAegXwhEAL2uWVBULQw9IusMYUyxJ1tpaVysD4FkMyAYAAHDgyhEAAIAD4QgAAMCBcAQAAOBAOAIAAHAgHAEAADgQjgAAABwIRwAAAA6EIwAAAAfCEQAAgMP/AQzPW5jDk25eAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "fig, ax = plt.subplots(figsize=(9.5, 7))\n", + "\n", + "ax.plot(xgrid, [g(x) for x in xgrid], label=\"$g$\", lw=2.0, alpha=1)\n", + "\n", + "ax.plot(xgrid, xgrid, 'k--', label=\"$45$\", lw=1.5, alpha=1)\n", + "\n", + "#ax.grid(True)\n", + "ax.set_xlim((0, 24))\n", + "ax.set_xlabel(r'$x$', fontsize=16)\n", + "ax.set_ylabel(r\"$x'$\", fontsize=16)\n", + "ax.legend(fontsize=16)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "fig, ax = plt.subplots(figsize=(9.5, 7))\n", + "\n", + "ax.plot(xgrid, [g(x) for x in xgrid], label=\"$g$\", lw=2.0, alpha=1)\n", + "ax.plot(xgrid, [g(x) - 1.5 for x in xgrid], \n", + " 'g-', label=\"$g - a$\", lw=1.0, alpha=1)\n", + "ax.plot(xgrid, [g(x) + 1.5 for x in xgrid], \n", + " 'g-', label=\"$g + b$\", lw=1.0, alpha=1)\n", + "\n", + "ax.plot(xgrid, xgrid, 'k--', label=\"$45$\", lw=1.5, alpha=1)\n", + "\n", + "#ax.grid(True)\n", + "ax.set_xlim((0, 24))\n", + "ax.set_xlabel(r'$x$', fontsize=16)\n", + "ax.set_ylabel(r\"$x'$\", fontsize=16)\n", + "ax.legend(fontsize=16)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Simulated distributions" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "@njit\n", + "def gen_marginal(w_init=1.0, num_reps=200, n=2000):\n", + "\n", + " w_sample = np.empty(num_reps)\n", + " for i in range(num_reps):\n", + " w = w_init \n", + " for t in range(n):\n", + " R = (1 + r) * exp(r_mu + r_sigma * np.random.randn())\n", + " w = R * s(w) + exp(mu + sigma * np.random.randn())\n", + " w_sample[i] = w\n", + " return w_sample\n", + "\n", + "w_sample = gen_marginal()" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def ecdf(x, sample):\n", + " return np.mean(sample <= x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### tracking marginals " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_grid = np.linspace(0, 500, 100)\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "n_vals = [1, 5, 1000]\n", + "\n", + "for n in n_vals:\n", + " w_sample = gen_marginal(w_init=200, num_reps=5000, n=n)\n", + " y_grid = [ecdf(x, w_sample) for x in x_grid]\n", + "\n", + " ax.plot(x_grid, y_grid, label=f\"$t = {n}$\")\n", + " \n", + "ax.set_xlabel(\"wealth\")\n", + "ax.legend(fontsize=14, loc=\"lower right\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### DKW bands" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "m = 10000\n", + "w_sample = gen_marginal(num_reps=m, w_init=200, n=100)\n", + "\n", + "alpha = 0.01\n", + "\n", + "eps = np.sqrt(np.log(2 / alpha) / (2 * m))\n", + "\n", + "x_grid = np.linspace(0, 500, 100)\n", + "y_grid = [ecdf(x, w_sample) for x in x_grid]\n", + "ya = y_grid - eps\n", + "yb = y_grid + eps\n", + "\n", + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x_grid, yb, alpha=0.7, label=\"$F_t^m + c(\\\\alpha, m)$\")\n", + "ax.plot(x_grid, y_grid, 'k-', label=\"$F_t^m$\")\n", + "ax.plot(x_grid, ya, alpha=0.7, label=\"$F_t^m - c(\\\\alpha, m)$\")\n", + "\n", + "ax.set_xlabel(\"wealth\")\n", + "ax.legend(fontsize=14, loc=\"lower right\")\n", + "\n", + "ax.set_title(f\"sample size = $m$\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### the stationary distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "w_sample = gen_marginal(num_reps=2000)\n", + "x_grid = np.linspace(0, 500, 100)\n", + "y_grid = [ecdf(x, w_sample) for x in x_grid]\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(x_grid, y_grid, label=\"$F_m$\")\n", + "ax.set_xlabel(\"wealth\")\n", + "ax.legend(fontsize=14, loc=\"lower right\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "w_sample = gen_marginal(w_init=200, n=100, num_reps=5000)\n", + "fig, ax = plt.subplots()\n", + "ax.hist(gen_marginal(), label=\"bin frequency\", density=True)\n", + "\n", + "ax.set_xlim((0, 500))\n", + "ax.set_xlabel(\"wealth\")\n", + "ax.legend(fontsize=14)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "from sklearn.neighbors import KernelDensity\n", + "w_sample = gen_marginal(w_init=200, n=100, num_reps=500)\n", + "kde = KernelDensity(kernel='gaussian').fit(w_sample[:, None])\n", + "log_dens = kde.score_samples(x_grid[:, None])\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(x_grid, np.exp(log_dens), label=\"NPKDE\")\n", + "ax.legend()\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "@njit\n", + "def lae(y, sample):\n", + " pr = 0.0\n", + " for x in sample:\n", + " pr += sk2(y, x)\n", + " return pr / len(sample)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_grid = np.linspace(0, 500, 100)\n", + "fig, ax = plt.subplots()\n", + "\n", + "y_grid = [lae(x, w_sample) for x in x_grid]\n", + "\n", + "ax.plot(x_grid, y_grid, label=\"$\\ell_t^m\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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lugN5H+9s/YeAqmm2jzLGlFtrd8Vel8Xe3xI7j9A8zbpn1caCjQAMBc7zVl2E1QWZTpYjckXLz8/n7NmzHDlyxOlSUp7X66WoqIjs7OzLXlfcMLDWVhpjHh5/YtgYU2Wt3R6nvRwojQVAZaz9EWPMl2KrrgAej71nZNnKy+7NDK3PXY8bF0cDhuwTB2DzMqdKEbniuVwuiouLnS5DZlnCsYlGtubHzdueoL0SqBwzHQZWT7D68Ljfjgh4AqzLWcUbPd3ccrYG+DUnyxERmXcpf9PZiI2LSzno95HV+obTpYiIzDuFQcymgs10u1wEzFHaenSlhIikFoVBzOaCzQB0BZo4es7R89kiIvNOYRCzPGs5Oe403gx4qH9bN5+JSGpRGMQYY9ict4E3/D4Gz+x3uhwRkXmlMBhj45IbqfV6cbe86nQpIiLzSmEwxqaCTVhj6LXHNCyFiKQUhcEYG/M3YoBmfxsnzzc5XY6IyLxRGIyR5ctiua+AgwEfpw8863Q5IiLzRmEwTsmSG4ZPItcqDEQkdSgMxtl8VSkRt5uhtpedLkVEZN4oDMbZungrAM3eOtra9UxkEUkNCoNxirOKyXNnsz/dS+1rv3S6HBGReaEwGMcYw01Lb+GVgJ+uo884XY6IyLxQGEzgPSv+E21uN5HWl5wuRURkXigMJnDjVTcCUOeuY7Cv2+FqRETmnsJgAvlp+Sz1FFCd7uXMG7rEVESSn8JgEluXbqPG76fpsKMPYRMRmRcKg0ncvvo2+lwuzjS/4HQpIiJzTmEwidKiUlwWTrrqYaDX6XJEROZUwjAwxpQbY8qMMQ9PtT02XTWF98Vdt5MyfZkUe5awP+Cl9a1fOV2OiMicihsGxphyAGttGIgYY8qm0h6bjvu+ROu+EpQsvY2Dfh+na37gdCkiInMq0Z7BVqA29roWKJlme7z3TXVZx3xo/XaixnC0+Tmwer6BiCSvRGEQHDedN832eO9LuKwxZocxptoYU93Y2Bi30LlwfeG7SLd+9vl7iTYenffPFxGZL4nCIALkXkZ7vPclXNZau9taW2qtLS0oKJjCx8wut8vNhuwbeC49jXP7vj/vny8iMl8ShcE+3tmCDwFV02yP976pLuuoX7/uI3S6XNSc+InTpYiIzJm4YWCtrQRC408Mj1wpFKe9HCgdc5L4kvdNtuyV5s7V78UbdfG6rYPuFqfLERGZE8YukBOjpaWltrq62pHPvvs799Laf4Afbf4TMko/4UgNIiIzYYzZb60tTfQ+3XQ2Be9Z/Z9p9Hh4+fXHnS5FRGROKAym4P7NH8BlYX/XQRgadLocEZFZpzCYgvyMIEuiS3g2zUP05PNOlyMiMusUBlN0beGdnPR5OVD9z06XIiIy6xQGU/RAyd0YC083PA+D/U6XIyIyqxQGU7R5STGFA0v4aYaH6PFfOF2OiMisUhhMw6bF5Zz3eHi++h+cLkVEZFYpDKZh540fxTdkeCryBvTr2cgikjwUBtNwTWEeRQPXEE730X34P5wuR0Rk1igMpmlL8Sfocbn46Wv/5HQpIiKzRmEwTQ9u3U72gJef9pyAnlanyxERmRUKg2lamZ9J7sAWXgn4qH/t206XIyIyKxQGM3Dz6gcAw+MHv6MnoIlIUlAYzMAntpRQ2JXP993d9J3e63Q5IiKXTWEwAyvyMsj2lNPidvPTl/+n0+WIiFw2hcEMPXDDr5Pf5+O7bYeweuiNiCxwCoMZuvO6q/B23MIRn5fqvd9wuhwRkcuiMJihgNfNTWs/Q+YQfLf2hzqRLCILmsLgMtx/42oKI6t5xjPEmbf+3elyRERmTGFwGa4uzMKf/gBu4J+rdahIRBYuhcFluu+GGwi1FfKDoRYaTr/gdDkiIjOSMAyMMeXGmDJjzMNTbR8/zxhTYow5bozZH/t5JDa/dez0QvSBjVdxofMTRIHHXvgzp8sREZmRuGFgjCkHsNaGgYgxpixR+yTL5FprV1trtwAPAY/GVnGPtXaLtbZiVns1jwJeN3ff+F7WtS+isq+OxvrXnC5JRGTaEu0ZbAVqY69rgZIptF8yLxYMI0LW2pH2oDEmNNmHG2N2GGOqjTHVjY2NCUp1zgM3raSu9V6GgMee/ROnyxERmbZEYRAcN503hfZJlzHG7LDWVo5pywVajDGPMgFr7W5rbam1trSgoCBBqc7JzfBx27tuY2NHFk90naCp+ajTJYmITEuiMIgw/IU9nfZ4y2wfOxH7so8wfDipPEEtV7TPbgtR1/QRBgx865cL9qiXiKSoRGGwj3e29ENA1RTaJ1zGGHPRHkPsENBIADRPu/IrzPLcdDas287Wjgwe7zjGyfP7nS5JRGTK4oZB7JBOaOTE8cixf2NM1WTtky1D7JDQmNU/zpiT0uMOHy1IO94b4ljDJ/BZy9d/OeHFVyIiVyRjF8gwCqWlpba6utrpMhJ68J/2kdn6X3k6t5nHbv5Ltq75kNMliUgKM8bst9aWJnqfbjqbZX9wxzXsvXA/iweH+Ku9XyVqo06XJCKSkMJgll27JJsbN5XwruZVHI528R81/8fpkkREElIYzIHf376WX0TuZ2PfAN84+C1ae/S8AxG5sikM5sDK/AzeX7qBJQ030WEH+atf/K7TJYmIxKUwmCNfvH0NT/bdzT0dLn7U/Covnnra6ZJERCalMJgji3MCPPjeNew//0lW9g/w35/7Mt0D3U6XJSIyIYXBHPqtW6/mfFYpH2xbybmhLv7upb9wuiQRkQkpDOZQms/Nl+9az7eaHuCejl6+c+JH7D33ktNliYhcQmEwx+7aeBVrQiH6Wj7Cqv4B/viXv0dbX5vTZYmIXERhMMeMMXzlw9fyvd7/xI7u5bQMdPJnz/wBC+XObxFJDQqDebBucTaffU+IPz3/GX6rY4Cqhpf596MLfigmEUkiCoN58nvb11JQtJRDkd/khp5e/vLlr3K4+bDTZYmIAAqDeRPwuvnGx97FT3rfxd09JeQM9PHFn++gpVd3J4uI8xQG8+jaJdn83va1/F7DfXy1K5OWvlb+IPx5BqIDTpcmIilOYTDPdr53NZtWFvGnTZ/nT1q7qW4+yF+9/D+cLktEUpzCYJ65XYZvfryEZt9S9vc9xANt7fzr0cd5/MjjTpcmIilMYeCAxTkBvvnxEv5f+2aui27nPd09fG3vV3nl/CtOlyYiKUph4JCbVufxR3eu4/P1v85vD66luL+P33/6C5xuP+10aSKSghQGDvrstlV8YNNS7j33Gb7WlQH9nXz+5w/R3NPsdGkikmIUBg4yxvA/79nM+hVL+K2mL/L1lj7qO+vY8dRnNGSFiMyrhGFgjCk3xpQZYx6eavsk81qNMfuNMY9Mdd2pIOB1860HSnEtKuZvOn6fv21s42RbLTt/9iAd/R1OlyciKSJuGBhjygGstWEgYowpS9QeZ5l7rLVbrLUVU1l3KlmU4eOfP30DRz1r+F7/7/PXja0caTnC536+Q4EgIvMi0Z7BVqA29roWKJlC+2TLBI0xoWmsG2PMDmNMtTGmurGxMUGpC9vy3HT+6dM38Ez/ep4e+m0eaWzmUPNBHnzq0zqHICJzLlEYBMdN502hfbJlcoEWY8yjU1w31trd1tpSa21pQUFBglIXvuuW5vB/P7WVPZ2bOcgO/ld9Iydaj/Kpp36T+q56p8sTkSSWKAwiDH+JT6d9wmViX+wRhg8JlU9h3SnphlW5/P39W/jfrTdwwLuTR+vqaWo/w/1P/gbHI8edLk9EklSiMNjHO1vwIaBqCu2XzIsd7imPzWuOs6wAt11TyN/edz1/3XQjL3p38ti5cwx2N3H/k/ezv2G/0+WJSBKKGwbW2kogNHJyN3ayF2NM1WTtkyzzOGNOEltrKydbtwy7a9NV/J9PlvC/Wm+myv0Q3zlzhrz+Hnb8fAc/O/kzp8sTkSRjFsoTt0pLS211dbXTZcy754418tC3q/l4+n6+OPS3/M6SJbzqjvKF67/AQxsfwhjjdIkicgUzxuy31pYmep9uOrvCbVtTwHcevJEf9N/Al6J/xN+fb+KuPss3X/0mFc9W0DvY63SJIpIEFAYLwNaVuXz/czdzwH89n+z9Y77S0scX27p46uRTfOqpT3G246zTJYrIAqcwWCCuLszk337rFqKLN3Nr21f48MBi/qbhAqdajlL+o3J+dPxHTpcoIguYwmABKcjy872H3k3pxmvZ1vhfCXpupvL0Sa4ZtHz5+S9T8WwF7f3tTpcpIguQwmCBSfO5+buPX8/nt1/HRy98hqf8D/IPJ9/mt7vhZyef4u4f3s2++n1OlykiC4zCYAEyxvA7t6/h739jC1/vuJ1PR/87D3QM8e26C/j6u3nwZw/y9eqv0zfU53SpIrJAKAwWsDuvu4of/842InmbeHfLV3AHbuCJY4cotxn846F/5O4f3s1LdS85XaaILAAKgwVuVX4G3//czZS/ZyN31T/E33h/my+fPcWjzV3Y3nZ2VO2g4tkKGruTe6A/Ebk8CoMk4Pe4+ZMPXsv3dtzEL/xl3Nb1FxQOLOEHR1/ncyafqlNV3PVvd7H7jd26L0FEJqQwSCLvDuXx5Be3cW/ZNj7Y8SX+Jvqb7Dj5Jv9e38ItaUv55qvf5MP//mF+XPtjojbqdLkicgVRGCQZv8fNF25fw09/91YOLP8kZT1fpa1/Gd9442ke688kaLx86bkvcd+P7+PFuhedLldErhAamyiJWWv5j9fq+IsfH+LdPc/y5+nfI2ewkSfX3crfuTo513OB0qJSdm7eyY2Lb9Q4RyJJaKpjEykMUkBH7wD/+5fH+ZfnD7PT9R885HmSKFGe2HA7jw020NjbzKaCTezctJNtS7cpFESSiMJALnGmpZu//vkRXnr9EH/g/QHlrmfo96bxw43v5//2naWuu571uet5aNND3F58Oy6jo4giC53CQCb19oVOvvn0MQ69sY8/9H6fO81e+gJBfnrdnfxD32lOdZ5lZfZK7r/2fj60+kOkedKcLllEZkhhIAmNhMLbb7zIH3oruc3UMODN4BfXvZ9/op1DkaPk+HO4Z+093HfNfRRlFDldsohMk8JApuztC5383dPHOHpgL//F9UM+6N4LxsVr68v4dmYaTzfW4DZu3r/q/fzG+t/guvzrnC5ZRKZIYSDTdra1m8eeP8nz+/ZxX/RJ7vM+S7rt5szS6/mXJSH+LfImXYNdbMzfyH3r7uP9K9+P3+13umwRiUNhIDPW1jPA4/vO8MSLb3Jzx8/4lO8XrLTnaA8E+cmam/hX28qJrjpy/Dl8MPRBPnL1R7gm9xqnyxaRCSgM5LINRS3hww1896WT9B9/nvs9Yd7vrsbDAHuXrOcH+Vfxi65TDEQHWJ+7njtX3ckdK+5gWdYyp0sXkZhZCwNjTDkQAUqstbum0j5+njEmCJTFFtlqra2Iva8VqAXCI/MmozBw1smmLv7lldNUVR9mW98v+YTvOdbZWlrdXp5csZmfpHk40F0HwHV513H7itu5vfh2VuWscrhykdQ2K2EQ+1LHWltpjNkB1Fprw/HageAE80KxebuNMY8Ax2Ovy8auLx6FwZWhb3CI8JsX+N6+01w4/iq/7nqBct9LFEYbOR3IIrzqeqo8loOdpwAI5YS4vXg4GK7Nu1Y3tInMs6mGgSdB+1ZgT+x1LVAChBO0542fN26PIgQ8GnsdNMaErLW1iQqVK4Pf4+auTVdx16arqG/bzI/fuIOHXjtLoO4VPjr4HPe99TKfsT2czSzkVys28zSWxw4+xrcOfIui9CLeV/w+3lf8PrYUbcHr8jrdHRGJSRQGwXHTeVNon3QZY0wIaBnz5Z8LtBhjHrXW7hz/4bE9ix0AxcXFCUqV+bY4J8Bnt4X47LYQp5q38OSBj/DAGycorP8VH2h7mY8eepZP0kdjYBHPryrhGZ+Xfzv2A/71rX8ly5fFLUtu4T1L38MtS28hPy3f6e6IpLREYRBh+At7Ou3xlikf+6Vvrd0NYIyJGGPKrbWVY98ca98Nw4eJEtQqDlqRl8Hnbl3N525dzdnWm6l6s4HPHThF+plnKBuq5vY39/IR00Wny8tzSzfxYvYinj+/l6dOPgXA+tz13LTkJm5ecjPXF16Pz+1zuEciqSWzLbZHAAANKklEQVRRGOzjnS39EFA1hfbgRMvEvuxHTjCXxdpaYgHQfBl9kCvMskXpfPqWVXz6llW0997Cy7Ut/O2xetre+hVrO/Zy26nX+LUz+4kCBzIKeOGqq3mlr5NvH/pnHjv4GAF3gJKiEm666ia2Lt7KNbnX4HEl+k9VRC7HVK4mehioAUJjtuSrrLXb47RfNC/25f8ow3sNABVANTByUmPCK5XG0gnk5FAX6eH5Y00cePMg7pPP8q7B17jFdZAC006XMTwXXE51wVKq3f0c7x1+VGe6J53rC69nc+FmNuZv5Lq86wgGxh+NFJGJ6D4DueJFo5Y3z7fzwrFGzhzZT+a559lqD3Cj6zCZppd6t5sXFq3k9dxC3nD3U9vbhGX4v9flWcvZmL+RTQWb2FywmXW567T3IDIBhYEsOINDUQ6ca6P6eAONR14mq/4FNg+9yRbXUTJMH53GUJ1RxOu5y3g7M403h9q40D+8s5nuSWdzwWauL7yeDfkb2JC3gby08dc7iKQehYEseNGo5XhjJ6+ebKT+aDXeuldY1nmQ613HWGaaAKhze3khuILXcxZxyDvI8f6W0b2HovQi1ueuZ13eOtYtWseaRWtYlrVMz2mQlKIwkKTU1TfIG2fbOHb8bXpOvEzahddY2X+U61wnyDWddBnDm34/1ZlFvJWZw3Gv5fRg+2hApHnSWJ2zmrW5a1m7aC1rgmtYHVytvQhJWgoDSRlNnX0cOBPh+Ntv0XvmVdKaD1Hcf5z1rlMsM010G8PbPi9v+rM4nJFPbZqfk6aXSLR3dB2L/IsIBUOsyllFKGf499XBqylKL9Jd07KgKQwkpTV39vFWfQe1Z87Refo1XI2HWdRxjKvtSdaas2SYXprcLo75fBzy53AsI8hpv5czpo/2aN/oejK9mawOrh4NiFU5qyjOKmZJ5hICnoCDPRSZGoWByDjWWurbezla38H5U0fpOnsQd9Nb5HSdYJU9w2pTR5bpocXlotbn5YgvwOG0RdQG/Jx1R2m1fRetryCtgOVZy1mWtYzirGKKs4tHf2f5shzqpcjFFAYiU2StpaG9j7cbOqivO0ln3VvYxmOkdZwkv/8MqzhPsblAtzvKSa+Xsx4PJ7xpnPBncc7n47zH0sLFQRH0B0eDYlnmMpZlLWNp5lKWZi6lKL0Ir1vjMsn8mK2B6kSSnjGGxTkBFucEYG0Bw+MvDusfjHK2tZu9ze1E6o7T33AE23qSFe2n2BQ5y+JoA8XmAtY1yFmPh9NeDye8Xo57Bznd3kG19y1+5hokyjsbXQZDflo+izMWU5ReRFFGEYXphRSmF1KU/s7rNE+aA/8akqq0ZyByGbr7Bzkf6ab5/Bk6G95msKkWV+Qk/s6zZPWeJ3+ogTxaaPYaznk81Hk81HvcnPP4OOMJ0Ojx0OSBHhO9ZN1Z3kwK04soSC8YDYqC9AIK0grIT8unML2Q/LR8jeMkcWnPQGQepPs8rC7MZnXhBmDDJe1DUUtjWxctdacYqK8lu+UMGW3nWdPVQKCzgcz+RhYNNZFpWmnzRmlwu7ng8dDodlPv7uSsp40L3lqOuF20uYaITnBhU44vh4L04YAoSCsgLy2PvEDe6O/ctFzyAnkEA0ENGy6TUhiIzCG3y7B4USaLF22ADZeGBQyfs+joHYAL50lvOEFR02nyIudY116Hr7sef6SJzMEWsoYiuNydNHrcNLpjPx43Te4O6tyNNHi8HHO7aHPDoJl4jz/Lm0luLCAW+RexKLCIoD9Ijj+HoD9Itj97eNqXQ44/h2x/Nn63fy7/ieQKoTAQcZgxhuw0H9krVsCKFXHf29vby8CFs7iazpHdUkdxWx22vQHTfQFfezNp/Y1kDEbw2DZ63f20uF20uN00u900u120ujpodjfQ5PZR63YTcbvocMFQnFspfC4vOb5sgoFF5PiDo+ExEiAjr7N92WT7ssnyZZHpyyTTm6m7vRcQhYHIAhIIBLiq+GquKr464XuH+rrJaDpPVnMDeS0N9LU3MdjZBN1NmN4Ins5WfAMRAoNtuKId4Opk0N1Pm8tFm9tNu8tFu8sVm26lzXWGVrebt10e2lwuOtyGwQT346W5/GS408n0ZZLtzyEnkEOmfzg0Mr2ZZPoyyfBmkOnNJMuX9c6PN2u0TYEyPxQGIknK7U8nf+lq8peuntL7rbV09fTS3tpIV1sTPW1N9Ha00t/ZwmB3BNvbjulrx93fjmegA99gO0Q7GaKbAVc3g6aPAfcQHS4XHS4XnS4XHS4z+rrT5aLJ5eLEaLthKMHd3QbwGx/prgAZ7rRYcGSRFcgmOxAkOy2HDF8mGZ4M0r3ppHvTyfBkjO6ZZHozyfBlkOHNwOfy6W7yOBQGIgIMH67KTE8jM70Ylk7/MbPWWvr6eulqb6G7rZnezlZ6O1rp64ow2N1GtLedaG8Hpq8T10AnroEO7GAXg7aTIdvFEH0MuPoYdA3Q54qOCZGLA6XLZWg2w/O7XC66XVPbc3BbQwAPAeMlYHz4XD4C7sDwjyeddF8aGd5MMvyZZAUyyQpkk+7LJs2fNRw0nuGwSfOkXfQTcAdwu9zT/ve60igMRGRWGGMIBNIIBJaSV7h0xuuJRi09vb30dHXQ2xWhr7uD/u42+rs7GOrtYLCnk2hfB9HeTkx/J9GeTgYG2hmIdjMQ7WLQ9tBn++mnnwHTT78Zot81SK8rSq8Luo2Lbpeh1xh6XIYe46J19LWhx+ViYJp7EB5r8OPCZ914jQcfHvwuL95Y6PjdfnzuAD5PAL8nDb8njTRfOum+jOEffyaZgWwy/BkEvAH8bn9smeHAmo/hTxQGInJFcbkMGelpZKSnQUHhrK57oL+Pnu5O+rra6e3uoL+ng77uTgZ6Oxno62Ggt4voQC/9fV30DHTQN9hD/2AX/UPdDER7GYz2MkAvg7aPQfoZZIAhM8ggAwy6hhgkyoArSq8x9LkMfWY4bDqMod8MT4/89LumHji7rvkyv/buj8/qv8V4CgMRSRlenx+vzw/BuRuy3Eaj9PX10NfTTX9PJ/29nQz0dDHU181gX+x3fw8Dfd309nfRN9g9+jM41Dv8E+1hMNrPoB1gyA6wKjfxBQOXS2EgIjKLjMtFIC2DQFoGUOB0OVOma7ZERCTxnoExphyIACXW2l1Tab+ceSIiMv/i7hnEvqyx1oaBiDGmLFH75cyb5b6JiMgUJTpMtBWojb2uBUqm0H4580RExAGJwiA4bnr8KfiJ2i9n3kWMMTuMMdXGmOrGxsYEpYqIyEwlCoMIkDvN9suZdxFr7W5rbam1trSgYOGclRcRWWgSnUDexztb8CGgagrtwcuYJyIiDoi7Z2CtrQRCIyd3Yyd7McZUTdZ+OfPmpIciIpLQgnnspTGmETg1w8XzgaZZLGchUJ9Tg/qc/C63vyustQmPsy+YMLgcxpjqqTwDNJmoz6lBfU5+89Vf3YEsIiIKAxERSZ0w2O10AQ5Qn1OD+pz85qW/KXHOQERE4kuVPQMREYlDYSAiIskfBsaY8tgoqQ87Xctsi/Wraty8S/qbLP8GxphgrC/lxphHxsxP2j7D6N+5LJX6PCKV+myMaTXG7Heqz0kdBsk+TPb4u7ZTYKjwe4Hc2N3rIwMZJnWfjTElwPZYX0qMMaFk7/OIWB9Csdep0Od7rLVbrLUVMP99TuowIPWGyU7qocJjAxeOXFkRAsIkf59rrLUVxpggUGutrSXJ+wxgjAnxTn8gBfoMBGP9HjGvfU72MEg4THaSmdFQ4QtN7H+YltgXY0r0GShleKRfSI0+h2J/3xGp0OdcoMUY82hsel77nOxhkHCY7CQzo6HCF6Bya+3O2OuU6HPssEBwzKNik7bPxpiyCQauTOo+w+ieb4Thwz/z/ndO+AzkBS7RENzJZqpDii9YxpjyMc/QLiPJ+xw7mXg8dnhs5IsgqfvM8NZxGcP9CcXOmyR1n40xOxje260EmmOz57XPSb1nkOzDZMe2HkrHnFRK6qHCY314JHbFxX5I/j4DjwK1I1+Osa3HpO5z7DxJmOHgC8bmJXWfgccZc0LYWls5333WHcgiIpLcewYiIjI1CgMREVEYiIiIwkBERFAYiIgICgMREUFhIDJrjDElIyNOjh1jZux8kSuVwkBkbujLXxYUhYHIGCPPh4gNFb0/9rrEGPOIMeaJ2M+OWPujI9Pj1vEwUBZrHxk6YGR6//z2SGRqFAYiF6uK3epfBlTHvszLgHRgj7X2HmCLtbbWWrszNl0xdgWxsZOqY+0jI422xAbXCyfBuPuShJJ9oDqR6QoDH2N4TJwnGA6CrUALsN0Ys5XYUNKxAdRKp7jekeGYm+O+S8QhCgORMay1NcaYLzH8IJnwmLHl9/POqJIjo0wGgd3AzonXJrJw6DCRyKVagOOx17lAVWwI6e0j5wkY3tL/GPClyVYSO58Qmqxd5EqiUUtFRER7BiIiojAQEREUBiIigsJARERQGIiICAoDERFBYSAiIigMREQE+P8vfVpE/zgNwQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "n_vals = [100, 500, 1000]\n", + "\n", + "for n in n_vals:\n", + " w_sample = gen_marginal(w_init=200, num_reps=500, n=n)\n", + " y_grid = [lae(x, w_sample) for x in x_grid]\n", + "\n", + " ax.plot(x_grid, y_grid, label=f\"$t = {n}$\")\n", + " \n", + "ax.set_xlabel(\"wealth\")\n", + "ax.legend(fontsize=14, loc=\"upper right\")\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Stationary Distributions\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "\n", + "w_sample = gen_wealth_ts(n=2000)\n", + "\n", + "y_grid = [lae(x, w_sample) for x in x_grid]" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(x_grid, y_grid, label=\"$\\\\ell_n^*$\")\n", + "\n", + "ax.set_xlabel(\"wealth\")\n", + "\n", + "ax.legend(fontsize=14, loc=\"upper right\")\n", + "\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}