Journal of Applied Mathematics and Stochastic Analysis
Volume 2008 (2008), Article ID 474623, 30 pages
Pricing Participating Products under a Generalized Jump-Diffusion Model
1Department of Mathematics and Statistics, Curtin University of Technology, Perth, Western Australia 6845, Australia
2Department of Mathematics, University of Bristol, Bristol BS8 1TW, UK
3Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Received 21 January 2008; Accepted 20 May 2008
Academic Editor: Vo Anh
Copyright © 2008 Tak Kuen Siu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes
of jump-diffusion models and Markovian regime-switching models. The Esscher
transform is employed to determine an equivalent martingale measure. Simulation
experiments are conducted to illustrate the practical implementation of the model
and to highlight some features that can be obtained from our model.