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Valuing the guaranteed minimum death benefit clause with partial withdrawals. (English) Zbl 1189.91066

In this paper, the authors determine the fair insurance charge for a guaranteed minimum death benefit (GMDB) contract allowing for partial withdrawals. Using a regime-switching model for the underlying stochastic process, the pricing of a GMDB is derived as a impulse control problem leading to a system of nonlinear PDEs. The interesting techniques developed in order to solve the final equations are likely to extend to other impulse control problems in finance. Popularity of GMDB contracts in the US and UK markets, along with the recent market turmoil, makes the pricing described in the paper particularly relevant. The rather technical (especially in the proofs) theoretical discussion is followed by a well-developed applicative part, where it is shown how valuable is the withdrawal feature in such contracts.

MSC:

91B30 Risk theory, insurance (MSC2010)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
49N25 Impulsive optimal control problems
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