Bayesian adaptive portfolio optimization (Q2771118)

The problem of portfolio optimization in stochastic control and mathematical finance has been dealt in this paper. The authors adopt a Bayesian approach for the utility maximization, by assuming that the unknown `drift' is an unobservable random variable, independent of the driving Brownian motion and with knovm probability distribution.NEWLINENEWLINENEWLINEUsing results from the filtering theory the optimization problem with partial observations to the case of a drift process which is adapted to observation process and well developed martingale methods are applied to obtain explicit formulae for the optimal portfolio process, the optimal wealth process and the value functions of the stochastic control problem. This is then treated buy using stochastic control and dynamic programming, which leads to generalized parabolic Monge-Ampère type equations. NEWLINENEWLINENEWLINEThese equations have been solved explicitly by using the results of sections 2 and 3. The problem of optimization is for an `insider' investor who can observe both the drift vector and the driving Brownian motion. It has been shown that the relative cost is asymptotically negligible as \(T\to\infty\). The optimal strategies and value functions under convex constraints on portfolio-proportion, including the constraints such as incomplete markets, prohibition or constraints on the short-selling of stocks, prohibition are constraints on borrowing.NEWLINENEWLINEFor the entire collection see [Zbl 0967.91001].