Valuation and hedging of life insurance liabilities with systematic mortality risk.

*(English)*Zbl 1201.91089Summary: This paper considers the problem of valuating and hedging life insurance contracts that are subject to systematic mortality risk in the sense that the mortality intensity of all policy-holders is affected by some underlying stochastic processes. In particular, this implies that the insurance risk cannot be eliminated by increasing the size of the portfolio and appealing to the law of large numbers. We propose to apply techniques from incomplete markets in order to hedge and valuate these contracts. We consider a special case of the affine mortality structures considered by M. Dahl [Insur. Math. Econ. 35, No. 1, 113–136 (2004; Zbl 1075.62095)], where the underlying mortality process is driven by a time-inhomogeneous Cox-Ingersoll-Ross (CIR) model. Within this model, we study a general set of equivalent martingale measures, and determine market reserves by applying these measures. In addition, we derive risk-minimizing strategies and mean-variance indifference prices and hedging strategies for the life insurance liabilities considered. Numerical examples are included, and the use of the stochastic mortality model is compared with deterministic models.

##### MSC:

91B30 | Risk theory, insurance (MSC2010) |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

91G80 | Financial applications of other theories |

##### Keywords:

stochastic mortality; affine mortality structure; equivalent martingale measure; risk-minimization; mean-variance indifference pricing; Thiele’s differential equation
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\textit{M. Dahl} and \textit{T. Møller}, Insur. Math. Econ. 39, No. 2, 193--217 (2006; Zbl 1201.91089)

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