In this paper, we consider a family of complete or incomplete Financial models such that the price processes of the Financial assets converge in distribution to those in a limit model. Different authors pointed out that we do not have necessarily convergence of the arbitrage pricing intervals in...

We are interested in general equilibrium incomplete markets, where the number of consumers is N, the number of goods is L, and the dimension of the space of admissible trades is K (the case of complete markets being then K=(L−1)). We prove that, if N≥K, any non-vanishing analytic function...

This paper examines qualitative properties of efficient insurance contracts in the presence of background risk. In order to get results for all strictly risk-averse expected utility maximizers, the concept of “stochastic increasingness” is used. Different assumptions on the stochastic...

In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer’s fixed point Theorem (1912), and is a refinement of several classical results in the standard...

This paper addresses partly an open question raised in the Handbook of Mathematical Economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete Markets (GEI) model. For a broad class of explicit asset structures, it is proved...

We study the dual formulation of the utility maximization problem in incomplete markets when the utility function is finitely valued on the whole real line. We extend the existing results in this literature in two directions. First, we allow for nonsmooth utility functions, so as to include the...

Given exogenously the price process of some assets, we constrain the price process of other assets, which are characterised by their final pay-offs. We deal with an incomplete market framework in a discrete time model and assume the existence of the equilibrium. In this setup, we derive...

Simulation has become a standard tool in statistics because it may be the only tool available for analysing some classes of probabilistic models. We review in this paper simulation tools that have been specifically derived to address statistical challenges and, in particular, recent advances in...

In this note we attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940's through its use today. We see how the earlier stages of the Monte Carlo (MC, not MCMC) research have led to the algorithms currently in use. More...

In this paper, we describe two computational methods for calculating the cumulative distribution function and the upper quantiles of the maximal difference between a Brownian bridge and its concave majorant. The first method has two different variants that are both based on a Monte Carlo...