We investigate the problem of maximizing the robust utility functional <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$\inf_{Q \in \mathcal{Q}} E_Qu(X)$</EquationSource> </InlineEquation>. We give the dual characterization for its solution for both a complete and an incomplete market model. To this end, we introduce the new notion of reverse f-projections and use techniques...</equationsource></inlineequation>

<Para ID="Par1">We study the gain of an insider having private information which concerns the default risk of a counterparty. More precisely, the default time τ is modelled as the first time a stochastic process hits a random threshold L. The insider knows this threshold (as it can be the case for the manager...</para>

<Para ID="Par1">This paper deals with an investment–consumption portfolio problem when the current utility depends also on the wealth process. Such problems arise e.g. in portfolio optimization with random horizon or random trading times. To overcome the difficulties of the problem, a dual approach is...</para>

This paper solves the following problem of mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the general, semimartingale model for incomplete markets, and to characterize it via the associated dual...