Coherent Measures of Risk

In this paper we study both market risks and nonmarket risks, without complete markets assumption, and discuss methods of measurement of these risks. We present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent." We examine the measures of risk provided and the related actions required by SPAN, by the SEC/NASD rules, and by quantile-based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.     

A Distance-Based Collective Weak Ordering

A group decision-making approach can be seen as a two stage process. The first stage allows for multi-cirteria evaluation of the alternatives and the second aims at deriving a collective weak ordering from the partial orderings supplied by the members after the first stage. The problem of combining the weak orderings to form a collective ranking is investigated. An axiomatic structure relating to the concept of distance between binary relations is developed. An algorithm for deriving the collective weak ordering is proposed, based on the idea of ranking first the least dominated alternatives.     

Insurance law and incomplete contracts

We analyze how insurance law can mitigate moral hazard by allowing insurers to reduce or cancel coverage in some circumstances. We consider an incomplete contract setting in which the insurer may obtain information related to the policyholder's behavior through a costly audit of the circumstances of the loss. Court decisions are based on a standard of proof such as the balance of probabilities. We show that an optimal insurance law brings efficiency gains compared to the no-audit case. We also highlight the conditions under which the burden of proof should be on the insured, provided that insurers are threatened with sanctions for bad faith.     

On the uniqueness of local equilibria

The purpose of this paper is to define a new notion of local equilibrium in an exchange economy, where the consumers face lower bounds on net trades. Then, we show that the local equilibrium is unique if the lower bounds are closed enough to 0. By the way, we also provide a convergence result of local equilibrium price toward Walras equilibrium price of a suitable tangent linear economy.     

On the Characterization of Efficient Production Vectors

In this paper we study the efficient points of a closed production set with free disposal. We first provide a condition on the boundary of the production set, which is equivalent to the fact that all boundary points are efficient. When the production set is convex, we also give an alternative characterization of efficiency around a given production vector in terms of the profit maximization rule. In the non-convex case, this condition expressed with the marginal pricing rule is sufficient for efficiency. Then we study the Luenberger’s shortage function. We first provide basic properties on it. Then, we prove that the above necessary condition at a production vector implies that the shortage function is locally Lipschitz continuous and the efficient points in a neighborhood are the zeros of it and conversely.     

A Distance-Based Collective Preorder Integrating the Relative Importance of the Group's Members

In this paper, we propose an aggregation procedure, which includes two steps. In the first one, the group's members elaborate individually a preorder (total or partial) on the alternatives set. These preorders can be obtained, for example, by applying a multicriterion aggregation procedure such as ELECTRE III, PROMETHEE I or II. In the second step, these individual preorders (total or partial) are aggregated into a collective preorder (total or partial). For this purpose, we first built a distance measure between pairs of binary relations in order to quantify the divergence between two preorders. Then we determine, for each pair of alternatives, the relative importance coefficients of the group's members by using a method based on subjective and objective components. These coefficients and the distance measure are finally exploited by an iterative algorithm in order to elaborate a collective preorder synthesizing the individual preorders.     

Is bioenergy trade good for the environment?

We analyze the impacts of bioenergy trade on greenhouse gas emissions using a two-good, three-factor model. Bioenergy is an agricultural good used as a substitute for fossil fuels in industry. Governments tax domestic pollution without international coordination. We assume that northern countries have higher labor productivity than southern ones and that agriculture is less pollution intensive than industry (after taxation). We show that whereas southern countries impose a lower tax rate than northern ones, they do not necessary have a competitive advantage in industry, and that compared to autarky, trade liberalization either increases or decreases worldwide emissions depending on regional comparative advantages.     

Discrete Walrasian exchange process

In an exchange economy, we define a discrete exchange process, which is Walrasian, since the trades are determined by the equilibrium allocation of the local equilibrium. We prove that this process attains a Pareto optimal allocation after a finite number of steps and the local equilibrium price then supports the Pareto optimal allocation. Furthermore, along the process, the allocation remains feasible and the utility of each consumer is non-decreasing.