Dynamic Capital Allocation With Distortion Risk Measures

Tsanakas and Barnett (2002) employed concepts from cooperative game theory (Aumann and Shapley, 1974) for the allocation of risk capital to portfolios of pooled liabilities, when distortion risk measures (Wang et al., 1997) are used. In this paper we generalise previously obtained results in three directions. Firstly, we allow for the presence of non-linear portfolios. Secondly, based on the concept of correlation order (Dhaene and Goovaerts, 1996) we proceed with discussing the links between dependence structures, capital allocation and pricing, as well as dropping a restrictive assumption on the continuity of probability distributions. Finally, we generalise the capital allocation methodology to a dynamic setting and conclude with a numerical example