We propose a generalization of the classical notion of the $V@R_{\lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an...

In the conditional setting we provide a complete duality between quasiconvex risk measures defined on $L^{0}$ modules of the $L^{p}$ type and the appropriate class of dual functions. This is based on a general result which extends the usual Penot-Volle representation for quasiconvex real valued...

Let χ be a family of stochastic processes on a given filtered probability space (Ω, "F", ("F"_"t")_{"t" is an element of "T"}, "P") with "T"⊆R_+. Under the assumption that the set "M"_"e" of equivalent martingale measures for χ is not empty, we give sufficient conditions for the existence...

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...

We discuss two issues about risk measures: we first point out an alternative interpretation of the penalty function in the dual representation of a risk measure; then we analyze the continuity properties of comonotone convex risk measures. In particular, due to the loss of convexity, local and...

Consider a dominated family of probability measures; we investigate the question of whether a single probability equivalent to the whole family exists. We show that for supermartingale, quasimartingale and martingale laws the answer is positive. We then provide a necessary and sufficient...