## The Annals of Applied Probability

### Optimal long term growth rate of expected utility of wealth

#### Abstract

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

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

Dates
First available in Project Euclid: 21 August 2002

https://projecteuclid.org/euclid.aoap/1029962817

Digital Object Identifier
doi:10.1214/aoap/1029962817

Mathematical Reviews number (MathSciNet)
MR1722286

Zentralblatt MATH identifier
0962.91036

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

#### Citation

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. https://projecteuclid.org/euclid.aoap/1029962817

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