On quasiconvex conditional maps : duality results and applications to Finance

Motivated by many financial insights, we provide dual representation theorems for quasiconvex conditional maps defined on vector space or modules and taking values in sets of random variables. These results match the standard dual representation for quasiconvex real valued maps provided by Penot and Volle. As a financial byproduct, we apply this theory to the case of dynamic certainty equivalents and conditional risk measures.