## The Annals of Applied Probability

### Risk-sensitive control and an optimal investment model II

#### Abstract

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

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

Dates
First available in Project Euclid: 17 July 2002

http://projecteuclid.org/euclid.aoap/1026915623

Digital Object Identifier
doi:10.1214/aoap/1026915623

Mathematical Reviews number (MathSciNet)
MR1910647

Zentralblatt MATH identifier
01906173

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

#### Citation

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. http://projecteuclid.org/euclid.aoap/1026915623.

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• PROVIDENCE, RI 02912 E-MAIL: whf@cfm.brown.edu INSTITUTE OF MATHEMATICS ACADEMIA SINICA
• NANKANG, TAIPEI TAIWAN REPUBLIC OF CHINA E-MAIL: sheusj@math.sinica.edu.tw