We prove the existence of Pareto optimal allocations within sets of acceptableallocations when decision makers have probabilistic sophisticated variational pref-erences dened on random endowments in L1.[...]

Abstract We introduce a generalised subgradient for law-invariant closed convex risk measures on L 1 and establish its relationship with optimal risk allocations and equilibria. Our main result gives sufficient conditions ensuring a non-empty generalised subgradient.

We investigate the problem of optimal risk sharing between agents endowed with cash-invariant choice functions which are law-invariant with respect to different reference probability measures. We motivate a discrete setting both from an operational and a theoretical point of view, and give...

We prove that in a discrete-time market model the lower arbitrage bound of an American contingent claim is itself an arbitrage-free price if and only if it corresponds to the price of the claim optimally exercised under some equivalent martingale measure.

The paper provides a comprehensive overview of modeling and pricing cyber insurance and includes clear and easily understandable explanations of the underlying mathematical concepts. We distinguish three main types of cyber risks: idiosyncratic, systematic, and systemic cyber risks. While for...

We investigate the problem of optimal risk sharing between agents endowed with cash-invariant choice functions which are law-invariant with respect to different reference probability measures. We motivate a discrete setting both from an operational and a theoretical point of view, and give...

We prove the existence of comonotone Pareto optimal allocations satisfying utility constraints when decision makers have probabilistic sophisticated variational preferences and thus representing criteria in the class of law invariant robust utilities. The total endowment is only required to be...

We prove the existence of Pareto optimal allocations within sets of acceptable allocations when decision makers have probabilistic sophisticated variational preferences dened on random endowments in L1.