Risk‐Sensitive Control and an Optimal Investment Model

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 −∞ < γ < 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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