Title: Expert opinions and utility maximization in a market with partially observable Gaussian drift
Authors: Ralf Wunderlich - BTU Cottbus-Senftenberg (Germany) [presenting]
Abstract: A continuous-time financial market with partial information on the drift is considered, and utility maximization problems are solved, which include expert opinions on the unobservable drift. Stock returns are driven by a Brownian motion and the drift depends on a factor process which is an Ornstein Uhlenbeck process. Thus, the drift is hidden and has to be estimated from observable quantities. If the investor only observes stock prices then the best estimate is the Kalman filter. However, to improve the estimate, an investor may also rely on expert opinions providing a noisy estimate of the current state of the drift. This reduces the variance of the filter and thus improves the expected utility. That procedure can be seen as a continuous-time version of the classical Black-Litterman approach. For the associated portfolio problem with logarithmic utility, explicit solutions are available in the literature. We consider the case of power utility. We apply dynamic programming techniques and solve the corresponding dynamic programming equation for the value function. Diffusion approximations for high-frequency discrete-time experts allow to simplify the problem and to derive more explicit solutions. We illustrate our findings by numerical results.