We examine a class of utility maximization problems with a non-necessarily law-invariant utility, and with a non-necessarily law-invariant risk measure constraint. Under a consistency requirement on the risk measure that we call Vigilance, we show the existence of optimal contingent claims, and...

Value-at-Risk (VaR) has become the most important benchmark for measuring risk in portfolios of different types of financial instruments. However, as reported by many authors, estimating VaR is subject to a high level of uncertainty. One of the sources of uncertainty stems from the dependence of...

In the classical expected utility framework, a problem of optimal insurance design with a premium constraint is equivalent to a problem of optimal insurance design with a minimum expected retention constraint. When the insurer has ambiguous beliefs represented by a non-additive probability...

Choice of contingent claims could reflect risk aversion or pessimism. Accordingly, the underlying, but hidden preferences might fit expected utility of customary von Neumann-Morgenstern form - or more generally, comply with a Choquet integral. This paper considers constrained choice and...

We give some Fubini's theorems (interversion of the order of integration and product capacities) in the framework of the Choquet integral for product sigma-algebras. Following Ghirardato this is performed by considering slice-comonotonic functions. Our results can be easily interpreted for...

Dow and Welang (1994) extended the notion of Nash equilibrium for two-player finite normal games when players are uncertainty on the behavior of his opponents. They showed the existence of equilibrium for any given degree of uncertainty however constant over all possible events, except the null...

This paper concerns the interpretation of equilibrium in non-additive beliefs in two-player normal form games. We argue that such equilibria involve beliefs and actions which are consistent with a lack of common knowledge of the game. Our argument rests on representation results which show that...

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space Ω, which include additivity and comonotonic additivity as extreme cases. Let E ⊆ 2Ω be a collection of subsets of Ω. Two functions x and y on Ω are...