Utility duality under additional information: conditional measures versus filtration enlargements

Abstract

The utility maximisation problem is considered for investors with anticipative additional information. We distinguish between models with conditional measures and models with enlarged filtrations. The dual functions of the maximal expected utility are determined with the help of f-divergences. We assume that our measures are absolutely continuous with respect to a local martingale measure (LMM), but not necessarily equivalent. Thus we do not exclude arbitrage.utility maximisation, additional information, enlargement of filtrations, conditional measures, convex conjugate function, dual function, f-divergence