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On systematic mortality risk and risk-minimization with survivor swaps. (English) Zbl 1224.91054

The authors deal with different financial markets, which contain a zero coupon bond and possibly one or more survivor swaps. The possibilities of hedging in these markets are studied. The authors review the mortality theory of M. Dahl and T. Møller [Insur. Math. Econ. 39, No. 2, 193–217 (2006; Zbl 1201.91089)] within a two-dimensional model with two portfolios, where the underling mortalities are correlated, and then consider the combined model. They introduce survivor swaps in the financial market and define their price process. The authors use the criterion of risk-minimization introduced by H. Föllmer and D. Sondermann [in: W. Hildenbrand (ed.) et al., Contributions to mathematical economics, Hon. G. Debreu, 206–223 (1986; Zbl 0663.90006)] for contingent claims and extended to payment processes by T. Møller [Finance Stoch. 5, No. 4, 419–446 (2001; Zbl 0983.62076)] to determine risk-minimizing strategies. The strategies illustrate how the combined insurance and financial risk can be hedged partly with bonds and survivor swaps. Finally, the strategies are compared numerically.

MSC:

91B30 Risk theory, insurance (MSC2010)
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