Title: Expert opinions and their approximation for multivariate stock returns with Gaussian drift
Authors: Dorothee Westphal - TU Kaiserslautern (Germany) [presenting]
Joern Sass - University of Kaiserslautern (Germany)
Ralf Wunderlich - BTU Cottbus-Senftenberg (Germany)
Abstract: A financial market with multivariate stock returns where the drift is an unobservable Ornstein-Uhlenbeck process is investigated. Information is obtained by observing stock returns and unbiased expert opinions. The optimal trading strategy of an investor maximizing expected logarithmic utility of terminal wealth depends on the conditional expectation of the drift given the available information, the filter. We investigate properties of the filters and their conditional covariance matrices. This includes the asymptotic behaviour for an increasing number of expert opinions on a finite time horizon and conditions for convergence on an infinite time horizon with regularly arriving expert opinions. In the situation where the number of expert opinions goes to infinity on a finite time horizon we distinguish between the case where experts have some minimal level of reliability and experts whose uncertainty increases with increasing frequency of information dates. The latter case leads to a diffusion approximation where the limiting diffusion can be interpreted as a continuous-time expert. This approximation for high-frequency experts thus allows to work with a simpler model in which more explicit solutions can be derived. We deduce properties of the value function using its representation as a functional of the conditional covariance matrices.