Marco Maggis

Dual Representation of Quasi-convex Conditional Maps ∗

We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued functions and the dual representation of conditional convex maps.

CONDITIONAL CERTAINTY EQUIVALENT

In a dynamic framework, we study the conditional version of the classical notion of certainty equivalent when the preferences are described by a stochastic dynamic utility u(x,t,ω). We introduce an appropriate mathematical setting, namely Orlicz spaces determined by the underlying preferences and thus provide a systematic method to go beyond the case of bounded random variables. Finally we prove a conditional version of the dual representation which is a crucial prerequisite for discussing the dynamics of certainty equivalents.

Model-free superhedging duality

In a model free discrete time financial market, we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path

Universal arbitrage aggregator in discrete-time markets under uncertainty

\omega \in \Omega

Complete duality for quasiconvex dynamic risk measures on modules of the

, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

L^{p}

In a model-independent discrete-time financial market, we discuss the richness of the family of martingale measures in relation to different notions of arbitrage, generated by a class S

-type

\mathcal{S}

RISK MEASURES ON P(R) AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION

of significant sets, which we call arbitrage de la classeS

Risk Measures on and Value at Risk with Probability/Loss Function

\mathcal{S}

The Fatou Closedness under Model Uncertainty

. The choice of S