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161 | 161 | "### The Bellman Operator\n", |
162 | 162 | "\n", |
163 | 163 | "We introduce the **Bellman operator** $ T $ that takes a function v as an\n", |
164 | | - "argument and returns a new function $ Tv $ defined by.\n", |
| 164 | + "argument and returns a new function $ Tv $ defined by\n", |
165 | 165 | "\n", |
166 | 166 | "$$\n", |
167 | 167 | "Tv(x) = \\max_{0 \\leq c \\leq x} \\{u(c) + \\beta v(x - c)\\}\n", |
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184 | 184 | "source": [ |
185 | 185 | "### Fitted Value Function Iteration\n", |
186 | 186 | "\n", |
187 | | - "Both consumption $ c $ and the state variable $ x $ are continous.\n", |
| 187 | + "Both consumption $ c $ and the state variable $ x $ are continuous.\n", |
188 | 188 | "\n", |
189 | 189 | "This causes complications when it comes to numerical work.\n", |
190 | 190 | "\n", |
|
648 | 648 | "cell_type": "markdown", |
649 | 649 | "metadata": {}, |
650 | 650 | "source": [ |
651 | | - "The fit is reasoable but not perfect.\n", |
| 651 | + "The fit is reasonable but not perfect.\n", |
652 | 652 | "\n", |
653 | 653 | "We can improve it by increasing the grid size or reducing the\n", |
654 | 654 | "error tolerance in the value function iteration routine.\n", |
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769 | 769 | "source": [ |
770 | 770 | "### Exercise 1\n", |
771 | 771 | "\n", |
772 | | - "We need to create a class to hold our primitives and return the right hand side of the bellman equation.\n", |
| 772 | + "We need to create a class to hold our primitives and return the right hand side of the Bellman equation.\n", |
773 | 773 | "\n", |
774 | 774 | "We will use [inheritance](https://en.wikipedia.org/wiki/Inheritance_%28object-oriented_programming%29) to maximize code reuse." |
775 | 775 | ] |
|
1008 | 1008 | } |
1009 | 1009 | ], |
1010 | 1010 | "metadata": { |
1011 | | - "date": 1609475202.1260993, |
| 1011 | + "date": 1610065566.4326456, |
1012 | 1012 | "filename": "cake_eating_numerical.rst", |
1013 | 1013 | "kernelspec": { |
1014 | 1014 | "display_name": "Python", |
|
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