This survey paper has three purposes: We first present in finite dimension, different approaches to the problem of uniqueness of Arrow-Debreu equilibrium when agents have additively separable utilities. We then study how, in the specific framework of a two period contingent good economy the...

In finite markets with short-selling, conditions on agents’ utilities insuring the existence of efficient allocations and equilibria are by now well understood. In infinite markets, a standard assumption is to assume that the individually rational utility set is compact. Its draw-back is that...

In order to analyse the effect of ambiguity and uncertainty aversion on equilibrium welfare, a two period, pure exchange one good economy is considered. Agents are Choquet-expected-utility maximizers with same convex capacity and strictly concave utility index. It is proven that equilibrium is...

A theory of individual decision and a general equilibrium theory in complete markets are provided, for the case of infinite state space when incomplete preferences are modelled by second order stochastic dominance (SSD). While, unlike the situation in the finite state space case, the demand of a...

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. No-arbitrage conditions are given in terms of risk adjusted priors. A sufficient condition for existence of efficient allocations is the overlapping...

In this paper we first prove an equilibrium existence theorem for finite dimensional economies with unbounded below consumption sets. We only assume that the individually rational utility set is compact and use the demand approach instead of the standard Negishi's approach. We next compare the...

An exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered. Sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each...

This paper provides a method to prove existence of solutions to some moral hazard problems with infinite set of outcomes. The argument is based on the concept of nondecreasing rearrangement and on a supermodular version of Hardy–Littlewood’s inequality. The method also provides qualitative...

This book explains key financial concepts, mathematical tools and theories of mathematical finance. It is organized in four parts. The first brings together a number of results from discrete-time models. The second develops stochastic continuous-time models for the valuation of financial assets...