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

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  • Fard, Farzad Alavi
  • Siu, Tak Kuen

Abstract

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.

Suggested Citation

  • Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
  • Handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:712-721
    DOI: 10.1016/j.insmatheco.2013.09.011
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    References listed on IDEAS

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    1. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
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    Citations

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    Cited by:

    1. Lin, Hongcan & Saunders, David & Weng, Chengguo, 2017. "Optimal investment strategies for participating contracts," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 137-155.
    2. Eckert, Johanna & Gatzert, Nadine & Martin, Michael, 2016. "Valuation and risk assessment of participating life insurance in the presence of credit risk," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 382-393.
    3. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2015. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," School of Economics Working Papers 2015-17, University of Adelaide, School of Economics.

    More about this item

    Keywords

    Participating products; Generalized jump–diffusion model; Markov-switching compensator; Esscher transform; Reduction of dimensionality; Collocation method;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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