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Regime-switching pure jump processes and applications in the valuation of mortality-linked products. (English) Zbl 1388.49020

Summary: In this paper, we study the pricing of longevity bonds and an insurance contract on multiple lives in a regime-switching market driven by an underlying continuous-time Markov chain. For modeling dependent mortality, we make use of a Markov chain and some shot noise processes with regime switching. By using a martingale method, we give semi-analytical expressions for the price of longevity bonds and the premium of an insurance contract on the \(k\)th person to die.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
44A10 Laplace transform
47D07 Markov semigroups and applications to diffusion processes
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
93E20 Optimal stochastic control

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