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Utility maximization with partial information: Hamilton-Jacobi-Bellman equation approach |
| BAI Lihua, GUO Junyi |
| School of Mathematical Sciences, Nankai University, Tianjin 300071, China; |
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Abstract This paper deals with the problem of maximizing the expected utility of the terminal wealth when the stock price satis?es a stochastic differential equation with instantaneous rates of return modelled as an Ornstein-Uhlenbeck process. Here, only the stock price and interest rate can be observable for an investor. It is reduced to a partially observed stochastic control problem. Combining the ?ltering theory with the dynamic programming approach, explicit representations of the optimal value functions and corresponding optimal strategies are derived. Moreover, closed-form solutions are provided in two cases of exponential utility and logarithmic utility. In particular, logarithmic utility is considered under the restriction of short-selling and borrowing.
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Issue Date: 05 December 2007
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