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Lithuanian Mathematical Journal

, Volume 54, Issue 4, pp 383–402 | Cite as

Regime-switching shot-noise processes and longevity bond pricing

  • Yinghui Dong
  • Kam C. Yuen
  • Chongfeng Wu
Article

Abstract

In this paper, we consider the valuation of longevity bonds under a regime-switching interest rate and a regimeswitching force of mortality model. The model assumes that the interest rate is driven by economic and environmental conditions described by a homogenous Markov chain and that the stochastic force of mortality is modeled by the sum of a regime-switching Gompertz–Makeham model and a regime-switching shot-noise process. Using the conditional Laplace transform of the regime-switching shot-noise process, we give a formula for the longevity bond price in terms of a couple of system partial differential equations. The pricing formula is also derived by using the concept of stochastic flows and the idea of change of measure.

Keywords

longevity bonds regime-switching Gompertz–Makeham model regime-switching shot-noise process forward measure stochastic flows 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsSuzhou University of Science and TechnologySuzhouPR China
  2. 2.Financial Engineering Research CenterShanghai Jiao Tong UniversityShanghaiPR China
  3. 3.Department of Statistics and Actuarial ScienceUniversity of Hong KongHong KongPR China

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