A stochastic control approach to robust duality in utility maximization.

Summary A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities: $$\text{Unknown environment 'myenumerate'}$$ In this paper we consider markets modeled by Itô-Lévy processes, and in the first part we give a new proof of the above result in this setting, based on the maximum principle in stochastic control theory. An advantage with our approach is that it also gives an explicit relation between the optimal portfolio $\varphi^*$ and the optimal measure $Q^*$, in terms of backward stochastic differential equations. In the second part we present robust (model uncertainty) versions of the optimization problems in (i) and (ii), and we prove a relation between them. In particular, we show explicitly how to get from the solution of one of the problems to the solution of the other. We illustrate the results with explicit examples.