Continuity of Utility-Maximization with Respect to Preferences
14 Pages Posted: 27 Apr 2009
Date Written: 2007-08
This paper provides an easily verifiable regularity condition under which the investor's utility maximizer depends continuously on the description of her preferences in a general incomplete financial setting. Specifically, we extend the setting of Jouini and Napp to include noise generated by a general continuous semi-martingale and to the case where the market price of risk process is allowed to be a general adapted process satisfying a mild integrability condition. This extension allows us to obtain positive results for both the mean-reversion model of Kim and Omberg and the stochastic volatility model of Heston. Finally, we provide an example set in Samuelson's complete financial model illustrating that without imposing additional regularity, the continuity property of the investor's optimizer can fail.
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