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.
BAI Lihua, GUO Junyi
. Utility maximization with partial information: Hamilton-Jacobi-Bellman equation approach[J]. Frontiers of Mathematics in China, 2007
, 2(4)
: 527
-537
.
DOI: 10.1007/s11464-007-0032-3