Excess based allocation of risk capital

Abstract

In this paper we propose a new rule to allocate risk capital to portfolios or divisions within a firm. Specifically, we determine the capital allocation that minimizes the excesses of sets of portfolios in lexicographical sense. The excess of a set of portfolios is defined as the expected loss of that set of portfolios in excess of the amount of risk capital allocated to them. The underlying idea is that large excesses are undesirable, and therefore the goal is to determine the allocation for which the largest excess is as small as possible. We show that this allocation rule yields a unique allocation, and that it satisfies some desirable properties. We also show that the allocation can be determined by solving a series of linear programming problems.

Compositional methods applied to capital allocation problems

“…The risk measure values are TVaR 99% (X sl ) = 364, 477, TVaR 99% (X surv ) = 11, 657 and TVaR 99% (X db ) = 6, 346, so the diversification benefit to share among agents is (364,477 + 11,657 + 6,356 = 382,356 = 6,124. Results Gulick et al (2012).…”

“…To provide a practical illustration of the application, we follow the example given in van Gulick et al (2012). The authors consider an insurance company offering three types of life insurance portfolios:…”

“…The results provided in van Gulick et al (2012) are as follows: the amount to be allocated is equal to K = TVaR 99% (X sl + X surv + X db ) = 376, 356, and the allocations derived from the principles are shown in Table 1. The relative capital allocation principles associated with the absolute principles, which belong to the simplex S 3 , are also presented.…”

“…A vast number of studies in the literature have been devoted to the analysis of capital allocation problems (see, among others, Denault, 2001;Kalkbrener, 2005;Tsanakas, 2009;Buch et al, 2011;van Gulick et al, 2012). Previous studies have focused on particular probability distributions of losses (Cossette et al, 2012(Cossette et al, , 2013, on alternative dependence structures between risks (Cai and Wei, 2014), on asymptotic allocations based on commonly used risk measures (Asimit et al, 2011) or on optimization function alterations in order to overcome limitations of the loss function minimization allocation criterion (Xu and Hu, 2012;Xu and Mao, 2013).…”

A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations

“…An overview of different capital allocation principles can be found in Koyhuoglu and Stoker (2002) and Urban et al (2003) 18 . Van Gulick et al (2012) define two key properties for a feasible allocation method. The risk contribution should not exceed the stand alone risk and it should not fall below the minimum loss that can occur from this position.…”