Risk capital allocation and cooperative pricing of insurance liabilities

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link

Dynamic capital allocation with distortion risk measures

“…We formalise these considerations using the correlation order on sets of random vectors with fixed marginals that was discussed by Dhaene and Goovaerts (1996) and Wang and Dhaene (1998). Using correlation order we also show that the capital allocation formula calculated by Tsanakas and Barnett (2002) holds in the more general setting considered in this paper.…”

“…The Aumann-Shapley (1974) value, which for positively homogenous and subadditive cost functions, such as coherent measures of risk, belongs to the fuzzy core (Aubin, 1981) of the game was shown to yield an appropriate risk capital allocation mechanism. Explicit formulae were obtained by Tasche (2000a), in the case that the risk measure is Expected Shortfall, and by Tsanakas and Barnett (2002), when distortion risk measures are used.…”

“…Allocation methodologies based on the fuzzy core are derived on the premise that no linear portfolio should be allocated more capital than its risk measure. Tsanakas and Barnett (2002) obtained an explicit allocation formula for the fuzzy core, in the case that distortion risk measures are used, and highlighted the relationship between capital allocation and the pricing of insurance liabilities.…”

Risk measurement in the presence of background risk

“…A capital allocation method for distortion risk measures, which satisfies (4) and (5) has been developed by Tsanakas and Barnett (2003) and Tsanakas (2004), who obtained the following allocation formula…”

“…When a distortion risk measure is used for determining the aggregate capital corresponding to the portfolio, explicit capital allocation formulas have been obtained by Tsanakas and Barnett (2003) and Tsanakas (2004).…”