On a Non-Standard Stochastic Control Problem

Details On a Non-Standard Stochastic Control Problem On a Non-Standard Stochastic Control Problem

2008-06-25

arxiv.org/abs/0806.4026v1

Economy

Quantitative Finance

Portfolio Management

Scientific paper

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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