Heterogeneous discounting in consumption-investment problems. Time consistent solutions
AbstractIn this paper we analyze a stochastic continuous time model in finite horizon in which agents discount the instantaneous utility function and the final function at constant but different instantaneous discount rates of time preference. Within this context we can model problems in which, when the time t approaches to the final time, the valuation of the final function increases compared with previous valuations in a way that cannot be explained by using a unique constant or a variable discount rate. We derive a dynamic programming equation whose solutions are time-consistent Markov equilibria. For this class of time preferences, we study the classical consumption and portfolio rules model (Merton, 1971) for CRRA and CARA utility functions for time- consistent agents, and we compare the different equilibria with the time-inconsistent solutions. The introduction of stochastic terminal time is also discussed.
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Bibliographic InfoPaper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 264.
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Date of creation: 2011
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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
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
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- Karp, Larry, 2004.
"Non-Constant Discounting in Continuous Time,"
Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series
qt7pr05084, Department of Agricultural & Resource Economics, UC Berkeley.
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- Karp, Larry, 2005. "Non-Constant Discounting in Continuous Time," Institute for Research on Labor and Employment, Working Paper Series qt0nn1t22z, Institute of Industrial Relations, UC Berkeley.
- Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 40(2), pages 351-401, June.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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