Comparison between Financial Theory and Cooperative Game Theory in Risk Capital Allocation

Abstract

We compare two prominent approaches to capital allocation in insurance firms. The financial theory approach includes Merton and Perold (1993) and Myers and Read (2001). The cooperative game theory approach utilizes concepts such as the Shapley value and the Aumann-Shapley value. We argue that, when an entire division is added or when the effect of a decision is discrete, the Shapley value approach provides an improvement over the Merton and Perold approach in that it properly accounts for the order in which divisions are added, and resoles the unallocated capital problem. When the effect of a decision is continuous, we show that the Auman-Shapley value approach not only provides game theoretic support for, but also conceptually extends, the Myers and Read approach.