Partially Observable Markov Decision Problems in Finance

Abstract

All the models which have been considered in Chapter 4 may also be treated in the case of partial information. Indeed models of this type occur somehow natural in mathematical finance because there are underlying economic factors influencing asset prices which are not specified and cannot be observed. Moreover, for example the drift of a stock is notoriously difficult to estimate. In this chapter we assume that the relative risk return distribution of the stocks is determined up to an unknown parameter which may change. This concept can also be interpreted as one way of dealing with model ambiguity. We choose two of the models from Chapter 4 and extend them to partial observation. The first is the general terminal wealth problem of Section 4.2 and the second is the dynamic mean-variance problem of Section 4.6.