Martin Schweizer
ETH Zurich
Abstract:
Portfolio choice is one of the classical problems from mathematical finance. One typical formulation is that one considers an agent who invests in a financial market to maximize his expected utility from consumption and/or terminal wealth. This problem and its solution are by now very well understood at the conceptual level, even if explicit solutions are rare.
Robust portfolio choice is concerned with the same problem when the investor is no longer certain about the underlying model. Hence he cannot take "the" expected utility, but must consider, for each possible model, the corresponding expected utility and try to find something which is optimal with respect to the model as well. A more precise formulation leads to a maximin (or minimax) problem where one maximizes over strategies and minimizes with respect to models.
One approach to study these problems is via convex duality. But if one wants more information about the dynamic behaviour of a solution, one will rather turn to stochastic control methods, and this leads to some interesting connections to backward stochastic differential equations. In the talk, we shall give an outline of this subject and try to explain how and where the different ideas come in. We also present some recent results, which are joint work with Giuliana Bordigoni and Anis Matoussi.