Abstract
This paper considers an asset-liability management problem under a continuous time Markov regime-switching jump-diffusion market. We assume that the risky stock’s price is governed by a Markov regime-switching jump-diffusion process and the insurance claims follow a Markov regime-switching compound poisson process. Using the Markowitz mean-variance criterion, the objective is to minimize the variance of the insurer’s terminal wealth, given an expected terminal wealth. We get the optimal investment policy. At the same time, we also derive the mean-variance efficient frontier by using the Lagrange multiplier method and stochastic linear-quadratic control technique.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bromson, R. (1991). Matrix methods: An introduction. London: Academic Press.
Chen, P., Yang, H. L., & Yin, G. (2008). Markowitzs mean-variance asset-liability management with regime switching: A continuous-time model. Insurance: Mathematics. Insurance: Mathematics and Economics, 43(3), 456–465.
Chiu, M. C., & Li, D. (2006). Asset and liability management under a continuous-time mean-variance optimization framework. Insurance: Mathematics and Economics, 39(3), 330–355.
Chiu, M. C., & Wong, H. Y. (2012). Mean-variance asset-liability management: Cointegrated assets and insurance liability. European Journal of Operational Research, 223(3), 785–793.
Elliott, R. J., & Siu, T. K. (2005). Option pricing and Esscher transform under regime switching. Annals of Finance, 1(4), 423–432.
Elliott, R. J., & Osakwe, C. J. U. (2006). Option pricing for pure jump processes with Markov switching compensators. Finance and Stochastics, 10(2), 250–275.
Elliott, R. J., & Siu, T. K. (2011). A stochastic differential game for optimal investment of an insurer with regime switching. Quantitative Finance, 11(3), 365–380.
Elliott, R. J., & Siu, T. K. (2013). Option pricing and filtering with hidden Markov-modulated pure-jump processes. Applied Mathematical Finance, 20(1), 1–25.
Elliott, R. J. (1982). Stochastic Calculus and Applications. New York: Springer.
Fleming, W. H., & Soner, H. M. (2006). Controlled Markov processes and viscosity solutions (2nd ed.). New York: Springer.
Hamilton, J. D. (1988). Rational-expectations econometric analysis of changes in regime: An investigation of the term structure of interest rates. Journal of Economic Dynamics and Control, 12(2), 385–423.
Li, D., & Ng, W. L. (2000). Optimal dynamic portfolio selection: Multi-Period mean-variance formulation. Mathematical Finance, 10(3), 387–406.
Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77–91.
Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory, 3(4), 373–413.
Sharpe, W. F., & Tint, L. G. (1990). Liabilities a new approach. Journal of Portfolio Management, 16(2), 5–10.
Xie, S. X. (2009). Continuous-time mean-variance portfolio selection with liability and regime switching. Insurance: Mathematics and Economics, 45(1), 148–155.
Xie, S. X., Li, Z. F., & Wang, S. Y. (2008). continuous-time portfolio selection with liability: Mean-variance model and stochastic LQ approach. Insurance: Mathematics and Economics, 42(3), 943–953.
Yao, H. X., Lai, Y. Z., & Li, Y. (2013). Continuous-time mean-variance asset-liability management with endogenous liabilities. Insurance: Mathematics and Economics, 52(1), 6–17.
Yi, L., Li, Z. F., & Li, D. (2008). Mutli-period portfolio selection for asset-liability management with uncertain investment horizon. Journal of Industrial and Management Optimization, 4(3), 535–552.
Yin, G., & Zhou, X. Y. (2004). Markowitz’s mean-variance portfolio selection with regime switching: From discrete-time models to their continuous-time limits. IEEE Transactions on Automatic Control, 49(3), 349–360.
Yong, J. M., & Zhou, X. Y. (1999). Stochastic controls: Hamiltonian systems and HJB equations. New York: Springer.
Zhang, X., Elliott, R. J., & Siu, T. K. (2012). A stochastic maximum principle for a Markov regime-switching jump-diffusion model and its application to finance. SIAM Journal on Control and Optimization, 50(2), 964–990.
Zhou, X. Y., & Li, D. (2000). Continuous-time mean-variance portfolio selection: A stochastic LQ framework. Applied Mathematics and Optimization, 42(1), 19–33.
Zhou, X. Y., & Yin, G. (2003). Markowitz’s mean-variance portfolio selection with regime switching: A continuous-time model. SIAM Journal on Control and Optimization, 42(4), 1466–1482.
Acknowledgments
The author thanks Xin Zhang for his helps. This work was supported partially by National Natural Science Foundation of China (11371020).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, J. Optimal Asset-Liability Management for an Insurer Under Markov Regime Switching Jump-Diffusion Market. Asia-Pac Financ Markets 21, 317–330 (2014). https://doi.org/10.1007/s10690-014-9187-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10690-014-9187-6