Coherent risk measure, equilibrium and equilibrium pricing

In this paper, we use a coherent risk measure to define Pareto equilibrium which is consistent with the one in microeconomic theory, and present necessary and sufficient conditions for this equilibrium in both a complete market and an incomplete market. These results are generalizations of those of Heath and Ku [Heath, D., Ku, H., 2004. Pareto equilibria with coherent measures of risk. Math. Finance 14 (2), 163–172]. Moreover, we also study Arrow–Debreu equilibrium and give the equilibrium price in terms of risk measures. Some examples are given to illustrate the results intuitively.