Abstracts

In a financial market with partial information we solve and compare utility maximization problems which include expert opinions on the underlying unobservable factors. We consider an investor who wants to maximize expected utility of terminal wealth obtained by trading in a financial market consisting of one riskless asset and several stocks. Stock returns are driven by a Brownian motion and the drift process is either an Ornstein-Uhlenbeck process (OUP) or a continuous time Markov chain (CTMC), independent of that Brownian motion. Thus the drift is hidden and has to be estimated from the observed stock prices. The best estimates given the observations are the Kalman and Wonham filters, respectively.
However, to improve the estimate, an investor may 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 expected utility. It can be seen as a continuous time version of the classical Black-Litterman approach. Frey/Gabih/Wunderlich (2012) solve the case of an underlying CTMC. As an approximation, also expert opinions arriving continuously in time can be introduced. This allows for more explicit solutions for the portfolio optimization problem. Davis/LLeo (2013) consider this approach for an underlying OUP.
In this talk we present and solve the utility maximization problems for the two missing cases, an underlying CTMC with continuous expert opinions and an OUP with time-discrete opinions. We analyze relations and differences of the continuous-time and discrete-time approaches and discuss the value of the additional information.

References:
Davis, M., Lleo, S. (2013): Black-Litterman in continuous time: The case for filtering. Quantitative Finance Letters, to appear.
Frey, R. Gabih, A., Wunderlich, R. (2012) Portfolio optimization under partial information with expert opinions. International Journal of Theoretical and Applied Finance 15/1.