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On a Non-Standard Stochastic Control Problem

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Author Info
Ivar Ekeland
Traian A Pirvu
Abstract

This paper considers the Merton portfolio management problem. We are concerned with non-exponential discounting of time and this leads to time inconsistencies of the decision maker. Following Ekeland and Pirvu 2006, we introduce the notion of equilibrium policies and we characterize them by an integral equation. The main idea is to come up with the value function in this context. If risk preferences are of CRRA type, the integral equation which characterizes the value function is shown to have a solution which leads to an equilibrium policy. This work is an extension of Ekeland and Pirvu 2006.

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File URL: http://arxiv.org/abs/0806.4026
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File URL: http://arxiv.org/pdf/0806.4026
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0806.4026.

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Date of creation: Jun 2008
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Handle: RePEc:arx:papers:0806.4026

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  1. Laibson, David, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 443-77, May.
  2. Loewenstein, George & Prelec, Drazen, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, MIT Press, vol. 107(2), pages 573-97, May. [Downloadable!] (restricted)
  3. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October. [Downloadable!] (restricted)
  4. Goldman, Steven M, 1980. "Consistent Plans," Review of Economic Studies, Blackwell Publishing, vol. 47(3), pages 533-37, April. [Downloadable!] (restricted)
  5. Peleg, Bezalel & Yaari, Menahem E, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Blackwell Publishing, vol. 40(3), pages 391-401, July. [Downloadable!] (restricted)
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