Risk Measures and Economic Capital for (Re)Insurers

Abstract

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 re-weighting of probability distributions are presented. It is shown how these different approaches relate to popular risk measures, such as VaR, Expected Shortfall, distortion risk measures and the exponential premium principle. The problem of allocating aggregate economic capital to sub-portfolios (e.g. insurers' lines of business) is then considered, with particular emphasis on marginal-cost-type methods. The relationship between insurance pricing and capital allocation is briefly discussed, based on concepts such as the opportunity and frictional costs of capital and the impact of the potential of default on insurance rates.

Keywords: risk measures, economic capital, risk capital, premium principles, choice under risk, solvency, capital allocation, insurance pricing, return on capital