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Non-constant discounting in finite horizon: The free terminal time case

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Author Info
Jesus Marin Solano
Jorge Navas Rodenes (Universitat de Barcelona)
Abstract

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. A simple example is used in order to illustrate the applicability of this HJB equation, by suggesting a method for constructing the subgame perfect equilibrium solution to the problem. Conditions for the observational equivalence with an associated problem with constant discounting are analyzed. Special attention is paid to the case of free terminal time. Strotzs model (an eating cake problem of a nonrenewable resource with non-constant discounting) is revisited.

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Publisher Info
Paper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 183.

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Length: 29 pages
Date of creation: 2007
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Handle: RePEc:bar:bedcje:2007183

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Postal: Espai de Recerca en Economia, Facultat de Ciències Econòmiques. Tinent Coronel Valenzuela, Num 1-11 08034 Barcelona. Spain.
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Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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