Risk Redistribution with Distortion Risk Measures∗

This paper studies optimal risk redistribution between firms, such as banks or insurance companies. The introduction of the Basel II regulation and the Swiss Solvency Test (SST) has increased the use of risk measures to evaluate financial or insurance risk. We consider the case where firms use a distortion risk measure (also called dual utility) to evaluate risk. The paper first characterizes all Pareto optimal redistributions. Thereafter, it characterizes competitive equilibria in settings where a well-functioning market exists and firms act as price-takers. It also characterizes optimal redistributions in cases where a well-functioning market does not exist, so that redistributions can only be obtained via Over-the-Counter trade. The paper contributes to the literature in two ways. First, when a well-functioning market exists, it presents three conditions that are jointly sufficient for existence of a unique equilibrium redistribution. This equilibrium’s redistribution and prices are provided in closed form. Second, when a well-functioning market does not exist, it identifies four properties that need to be satisfied for a redistribution to be perceived as “fair” by all involved parties. It shows that there is a unique such risk redistribution. This redistribution coincides with the competitive equilibrium.