Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach

• Published in: Insurance, mathematics & economics mathematics & economics, 2013-11, Vol.53 (3), p.712-721
• Main Authors: Fard, Farzad Alavi, Siu, Tak Kuen
• Format: Article
• Language: English
• Subjects: Collocation method; Equivalence; Esscher transform; Generalization; Generalized jump–diffusion model; Life insurance; Markov analysis; Markov-switching compensator; Markovian processes; Mathematical models; Numerical analysis; Participating products; Pricing; Reduction of dimensionality; Studies; Valuation; Valuation methods
• ISSN: 0167-6687; 1873-5959
• DOI: 10.1016/j.insmatheco.2013.09.011

We propose a model for the valuation of participating life insurance products under a generalized jump–diffusion model with a Markov-switching compensator. The Esscher transform is employed to determine an equivalent martingale measure in the incomplete market. The results are further manipulated through the utilization of the change of numeraire technique to reduce the dimensions of the pricing formulation. This paper is the first that extends the technique for a generalized jump–diffusion process with a Markov-switching kernel-biased completely random measure, which nests a number of important and popular models in finance. A numerical analysis is conducted to illustrate the practical implications. •Participating products are priced under generalized jump–diffusion model.•Markov-switching model is used to capture the structural changes in the economy.•The Esscher transform is employed to determine an equivalent martingale measure.•The change of numeraire technique is used to reduce the dimensions of the model.•The Collocation method is used for the numerical analysis of the PIDE.