The Annals of Applied Probability

Optimal long term growth rate of expected utility of wealth

Wendell H. Fleming and Shuenn-Jyi Sheu

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An optimal investment policy model for the long term growth of expected utility of wealth is considered. The utility function is HARA with exponent $-\infty < \gamma < 1$. The problem can be reformulated as an infinite time horizon, risk sensitive control problem. Then the dynamic programming equations for different HARA exponents and different policy constraints are studied. We obtain some estimates for the solution of each equation. This can be used to derive an optimal policy with some interesting properties.

Article information

Ann. Appl. Probab., Volume 9, Number 3 (1999), 871-903.

First available in Project Euclid: 21 August 2002

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Zentralblatt MATH identifier

Primary: 90A09 93E20: Optimal stochastic control
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 90A19

Long term growth rate Ornstein-Uhlenbeck process risk sensitive control dynamical programming equation optimal policy


Fleming, Wendell H.; Sheu, Shuenn-Jyi. Optimal long term growth rate of expected utility of wealth. Ann. Appl. Probab. 9 (1999), no. 3, 871--903. doi:10.1214/aoap/1029962817.

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