Regime-switching shot-noise processes and longevity bond pricing

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 stochasti...

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Bibliographic Details
Published in:Lithuanian mathematical journal 2014-10, Vol.54 (4), p.383-402
Main Authors: Dong, Yinghui, Yuen, Kam C., Wu, Chongfeng
Format: Article
Language:English
Subjects:
Actuarial Sciences
Economic models
Interest rates
Laplace transforms
Longevity
Markov analysis
Markov chains
Mathematics
Mathematics and Statistics
Mortality
Noise
Number Theory
Ordinary Differential Equations
Partial differential equations
Pricing
Probability Theory and Stochastic Processes
Shot
Switching
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Summary: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.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-014-9251-y