Consumption and portfolio rules for time-inconsistent investors |
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Authors: | Jesús Marín-Solano Jorge Navas |
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Institution: | Dept. Matemàtica Econòmica, Financera i Actuarial, Universitat de Barcelona, Av. Diagonal 690, E-08034 Barcelona, Spain |
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Abstract: | This paper extends the classical consumption and portfolio rules model in continuous time Merton, R.C., 1969. Lifetime portfolio selection under uncertainty: The continuous time case. Review of Economics and Statistics 51, 247–257, Merton, R.C., 1971. Optimum consumption and portfolio rules in a continuous time model. Journal of Economic Theory 3, 373–413] to the framework of decision-makers with time-inconsistent preferences. The model is solved for different utility functions for both, naive and sophisticated agents, and the results are compared. In order to solve the problem for sophisticated agents, we derive a modified HJB (Hamilton–Jacobi–Bellman) equation. It is illustrated how for CRRA functions within the family of HARA functions (logarithmic and power utilities) the optimal portfolio rule does not depend on the discount rate, but this is not the case for a general utility function, such as the exponential (CARA) utility function. |
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Keywords: | Finance Consumption and portfolio rules Non-constant discounting Time inconsistency Naive and sophisticated agents Dynamic programming |
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