About: 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.   Goto Sponge  NotDistinct  Permalink

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  • 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.
Subject
  • Senescence
  • Actuarial science
  • Differential equations
  • Markov models
  • Mathematical physics
  • Mathematical finance
  • Fractals
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