Non-constant discounting in finite horizon: the free terminal time case. (English) Zbl 1168.49025
Summary: This paper derives the HJB (Hamilton-Jacobi-Bellman) equation for sophisticated agents in a finite horizon dynamic optimization problem with non-constant discounting in a continuous setting, by using a dynamic programming approach. Special attention is paid to the case of free terminal time. Strotz’s model (a cake-eating problem of a non-renewable resource with non-constant discounting) is revisited. A consumption-saving model is used to illustrate the results in the free terminal time case.
MSC:
| 49L20 | Dynamic programming in optimal control and differential games |
| 91B64 | Macroeconomic theory (monetary models, models of taxation) |
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