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Risk Margin for a Non-Life Insurance Run-Off

By Mario V. Wüthrich, Paul Embrechts and Andreas Tsanakas


For solvency purposes insurance companies need to calculate so-called best-estimate reserves and a risk margin for non-hedgeable insurance-technical risks. In actuarial practice, often the calculation of the risk margin is not based on a sound model but various ad-hoc methods are used. In the present paper we properly define these notions and we introduce insurance-technical probability distortions. We describe how the latter can be used to calculate a risk margin for a non-life insurance run-off in a mathematical consistent way. Key words. Claims reserving, best-estimate reserves, run-off risks, risk margin, market value margin, one-year uncertainty, claims development result, market-consistent valuation. 1 Market-consistent valuation The main task of an actuary is to predict and value insurance liability cash flows. These predictions and valuations form the basis for premium calculations as well as for solvency considerations of an insurance company. As a consequence and in order to be able to successfully run the insurance business, actuaries need to have a good understanding of such cash flows. In most situations, insurance cash flows are not traded on deep and liquid financial markets. Therefore valuation of insurance cash flows basically implies the pricing in an incomplete financial market setting. Article 75 of the Solvency II Framework Directive (Directive 2009/138/EC) states “liabilities shall be valued at the amount for which they could be transferred, or settled, between two knowledgeable willing parties in an arm’s length transaction”. The general understanding is that this amount should consist of two components, namely the so-called best-estimates reserve

Year: 2011
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