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Risk-sensitive control and an optimal investment model. II. (English) Zbl 1074.93038

Summary: 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 dynamic programming equation. Then an optimal (or approximately optimal) Markovian investment policy can be derived.
For Part I see [Math. Finance 10, No. 2, 197–213 (2000; Zbl 1039.93069)].

MSC:

93E20 Optimal stochastic control
60H30 Applications of stochastic analysis (to PDEs, etc.)
91G80 Financial applications of other theories

Citations:

Zbl 1039.93069
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References:

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[29] 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
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