Large economies with differential information but without free disposal

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy, Moreno and Shitovitz (2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis, Muir and Yannelis (2002)). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (2001) are still valid without freedisposal. Then we define an incentive compatibility property motivated by the issue of contracts’ execution and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of competitive or core allocations are enforceable.

Contract enforcement and incentive compatibility in large economies with differential information: the role of exact feasibility

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy, Moreno and Shitovitz (2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis, Muir and Yannelis (2002)). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (2001) are still valid without free-disposal. Then we define an incentive compatibility property motivated by the issue of contracts’ execution and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of a competitive or core allocations are enforceable.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.

Valuation equilibrium with crubs

This paper considers model worlds in which there are a continuum of individuaIs who form finite sized associations to undertake joint activities. We show that if there are a finite set of types and the commodity space contains lotteries, then the c1assicaI equilibrium results on convex economies can be reinterpreted to apply. Furthermore, in this lottery economy deterministic aIlocations (that is, degenerate lotteries) are generally not Pareto optimal, nor are they equilibria. In the interests of making the model seem more "natural," we show that the set of equilibria in a decentraIization in which individuaIs first gamble over vaIue transfers and then trade commodities in a deterministic competitive market economy are equivalent to those of our competi tive economy with a lottery commodity space.

Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures

We consider risk-averse convex stochastic programs expressed in terms of extended polyhedral risk measures. We derive computable con dence intervals on the optimal value of such stochastic programs using the Robust Stochastic Approximation and the Stochastic Mirror Descent (SMD) algorithms. When the objective functions are uniformly convex, we also propose a multistep extension of the Stochastic Mirror Descent algorithm and obtain con dence intervals on both the optimal values and optimal solutions. Numerical simulations show that our con dence intervals are much less conservative and are quicker to compute than previously obtained con dence intervals for SMD and that the multistep Stochastic Mirror Descent algorithm can obtain a good approximate solution much quicker than its nonmultistep counterpart. Our con dence intervals are also more reliable than asymptotic con dence intervals when the sample size is not much larger than the problem size.