The Annals of Applied Probability

Risk-sensitive control and an optimal investment model II

W. H. Fleming and S. J. Sheu

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We consider an optimal investment problem proposed by Bielecki and Pliska. The goal of the investment problem is to optimize the long-term growth of expected utility of wealth. We consider HARA utility functions with exponent $-\infty< \gamma< 1$. The problem can be reformulated as an infinite time horizon risk-sensitive control problem. Some useful ideas and results from the theory of risk-sensitive control can be used in the analysis. Especially, we analyze the associated dynamical programming equation. Then an optimal (or approximately optimal) Markovian investment policy can be derived.

Article information

Ann. Appl. Probab. Volume 12, Number 2 (2002), 730-767.

First available in Project Euclid: 17 July 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 90A09 93E20: Optimal stochastic control
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Risk-sensitive stochastic control optimal investment model long-term growth rate dynamical programming equation Ricatti equation


Fleming, W. H.; Sheu, S. J. Risk-sensitive control and an optimal investment model II. Ann. Appl. Probab. 12 (2002), no. 2, 730--767. doi:10.1214/aoap/1026915623.

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