This contribution relates to the use of risk measures for determining (re)insurers' economic capital requirements. Alternative sets of properties of risk measures are discussed. Furthermore, methods for constructing risk measures via indifference arguments, representation results and...

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...

The Aumann-Shapley (1974) value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault (2001). We obtain an explicit formula for the Aumann-Shapley value, when the risk measure is given by a distortion...

A distortion-type risk measure is constructed, which evaluates the risk of any uncertain position in the context of a portfolio that contains that position and a fixed background risk. The risk measure can also be used to assess the performance of individual risks within a portfolio, allowing...

The theory and practice of risk measurement provides a point of intersection between risk management, economic theories of choice under risk, financial economics and actuarial pricing theory. This paper provides a review of these interrelationships, from the perspective of an insurance company...

We discuss classes of risk measures in terms both of their axiomatic definitions and of the economic theories of choice that they can be derived from. More specifically, expected utility theory gives rise to the exponential premium principle, proposed by Gerber (1974), Dhaene et al. (2003),...

An exchange economy is considered, where agents (insurers/banks) trade risks. Decision making takes place under distorted probabilities, which are used to represent either rank-dependence of preferences or ambiguity with respect to real-world probabilities. Pricing formulas and risk allocations,...

It is shown that for elliptically distributed bivariate random vectors, the riskiness and dependence strength of random portfolios, in the sense of the univariate convex and bivariate concordance stochastic orders respectively, can be simply characterised in terms of the vector's...

Internal capital models are increasingly used across the insurance business, including reinsurance optimization, risk appetite and business planning. While this expansion is well documented, less is known about what modelers do in practice, in order to embed capital models within their...