Dynamic capital allocation with distortion risk measures

Tsanakas and Barnett [Insurance: Mathematics and Economics 33 (2003) 239] employed concepts from cooperative game theory [Aumann and Shapley, Values of Non-Atomic Games. Princeton University Press, Princeton] for the allocation of risk capital to portfolios of pooled liabilities, when distortion risk measures [Insurance: Mathematics and Economics 21 (2) (1997) 173] 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 [ASTIN Bulletin 26 (2) (1996) 201] 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.