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May 2002 Risk-sensitive control and an optimal investment model II
W. H. Fleming, S. J. Sheu
Ann. Appl. Probab. 12(2): 730-767 (May 2002). DOI: 10.1214/aoap/1026915623


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.


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W. H. Fleming. S. J. Sheu. "Risk-sensitive control and an optimal investment model II." Ann. Appl. Probab. 12 (2) 730 - 767, May 2002.


Published: May 2002
First available in Project Euclid: 17 July 2002

zbMATH: 1074.93038
MathSciNet: MR1910647
Digital Object Identifier: 10.1214/aoap/1026915623

Primary: 90A09 , 93E20
Secondary: 60H30

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

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 2 • May 2002
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