Equilibrium with coherent risk

Abstract

This paper is the continuation of "Pricing with coherent risk" and deals with further applications of coherent risk measures to problems of finance. First, we study the optimization problem. Three forms of this problem are considered. Furthermore, the results obtained are applied to the optimality pricing. Again three forms of this technique are considered. Finally, we study the equilibrium problem both in the unconstrained and in the constrained forms. We establish the equivalence between the global and the competitive optima and give a dual description of the equilibrium. Moreover, we provide an explicit geometric solution of the constrained equilibrium problem. Most of the results are presented on two levels: on a general level the results have a probabilistic form; for a static model with a finite number of assets, the results have a geometric form.