Eduard Kromer, University of California, Berkeley
Abstract: The problem of optimal risk sharing between two or more agents has applications in different areas of finance, particularly the areas of actuarial science and portfolio theory are of great importance. The problem formulation is the following: Consider m agents, each with an initial random endowment. These initial endowments add up to an aggregate risky position. Now the optimal risk sharing problem is to find an optimal allocation of this aggregate position such that the allocated risk is acceptable to each agent. We study an optimal risk sharing problem which is based on utility functions that depend on multiple different (convex) risk measures of the agents. In comparison to similar approaches this setting introduces more flexibility in terms of the number of risk measures the agents may prefer to minimize simultaneously. This setting comprises situations where agents can incorporate different risk measures where some of them reflect their own preferences and others reflect requirements from regulators. In this context we study the properties of so called coalitional risk measures. These functionals will be the key to a characterization result for solutions to the proposed optimal risk sharing problem with multiple risk criteria.
Joint work with Ludger Overbeck.