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Bulletin n°26 / vol. 13 / Juillet 2013 - Décembre 2013 Le BFA sur internet
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From game theory to solvency quantile calculation: capital allocation with use in non-life insurance

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Capital allocation is an instrument for managing risk in an insurance company, especially by showing the diversification effect between lines of business. Based on a practical application of game theory, this article proposes a practical mapping between coherent measure of risk and coherent capital allocation. In terms of risk measure, VaR and TVaR have been selected, from which quantile-based allocation formulae can be derived. These formulae require the use of simulation, and it is shown here that the algorithm of Ruhm, Mango and Kreps (RMK) is especially adapted. Capital allocation has been applied in this article in two solvency calculation internal models. In this case, internal modelling of risks may change from one model to another. However, VaR shows more consistent results over time than TVaR. It is suggested that not only (axiomatic) coherent allocation, but also consistent allocation needs to be considered.