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Factor risk quantification in annuity models |
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| Affiliation: | 1. Department of Actuarial Sciences, Hacettepe University, Ankara, Turkey;2. Maxwell Institute for Mathematical Sciences, and Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, United Kingdom;1. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong;2. Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, PR China;1. Department of Statistics, Wuhan University of Technology, Wuhan, 430070, PR China;2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, PR China |
| Abstract: | Calculation of risk contributions of sub-portfolios to total portfolio risk is essential for risk management in insurance companies. Thanks to risk capital allocation methods and linearity of the loss model, sub-portfolio (or position) contributions can be calculated efficiently. However, factor risk contribution theory in non-linear loss models has received little interest. Our concern is the determination of factor risk contributions to total portfolio risk where portfolio risk is a non-linear function of factor risks. We employ different approximations in order to convert the non-linear loss model into a linear one. We illustrate the theory on an annuity portfolio where the main factor risks are interest-rate risk and mortality risk. |
| Keywords: | Risk capital allocation Risk measures Risk contribution Life insurance Hoeffding decomposition Taylor expansion |
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