Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such...

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual...

Given a convex risk measure on $L^\infty$ having the Lebesgue property, we construct a solid space of random variables on which the original risk measure is extended preserving the Lebesgue property (on the entire space). This space is an order-continuous Banach lattice, and is maximum among all...

The existence of optimal strategy in robust utility maximization is addressed when the utility function is finite on the entire real line. A delicate problem in this case is to find a "good definition" of admissible strategies to obtain an optimizer. Under certain assumptions, especially a...

The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual...

Given a monotone convex function on the space of essentially boundedrandom variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such...

We discuss the problem of exponential hedging in the presence of model uncertainty expressed by a set of probability measures. This is a robust utility maximization problem with a contingent claim. We first consider the dual problem which is the minimization of penalized relative entropy over a...

We consider the pointwise supremum of a family of convex integral functionals of essentially bounded random variables, each associated to a common convex integrand and a respective probability measure belonging to a dominated weakly compact convex set. Its conjugate functional is analyzed,...

We provide an alternative method for analysis of multifractal properties of time series. The new approach takes into account the behaviour of the whole multifractal profile of the generalized Hurst exponent $h(q)$ for all moment orders $q$, not limited only to the edge values of $h(q)$...