INF-CONVOLUTION OF DYNAMIC RISK MEASURES AND OPTIMAL RISK TRANSFER

Nicole El Karoui
(joint work with Pauline Barrieu)

Abstract

We develop a methodology to optimally design a financial issue to hedge non-tradable risk on financial markets. Economic agents assess their risk using monetary risk measure. The inf-convolution of convex risk measures is the key transformation in solving this optimization problem. When agents’risk measures only differ from a risk aversion coefficient, the optimal risk transfer is amazingly equal to a proportion of the initial risk. For dynamic risk measures defined through their local specifications using Backward Stochastic Differential equation, their inf-convolution is equivalent to that of their associated drivers. In this case, it is also possible to characterize the optimal risk transfer.