Regime-switching pure jump processes and applications in the valuation of mortality-linked products

ABSTRACT

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 kth person to die.

KEYWORDS:

• Longevity bond
• Markov chain
• multiple-life model
• shot noise process with regime switching

MATHEMATICS SUBJECT CLASSIFICATION:

• 49K15
• 44A10
• 47D07

Funding

The research of Yinghui Dong is supported by the Natural Science Foundation of Jiangsu Province [grant number. BK20170064] and QingLan project. The research of Kam Chuen Yuen was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China [grant number HKU17329216] and the Society of Actuaries [grant number CAE 2013]. Any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the SOA. The research of Guojing Wang is supported by the National Natural Science Foundation of China (Grant No. 11371274).