Abstract
This paper investigates the optimal portfolio investment policies of an insurer with Markov-modulated jump-diffusion risk process. Assume that there are two asset available for the insurer: a risk-free asset and a risky asset. The market interest rate, the drift and the volatility of the risky asset, and the premium rate of the insurer and claim arrival intensity switch over time according to transitions of the Markov chain. Given an insurer maximizing utility from terminal wealth, we present a verification result for portfolio problems, and obtain the explicit forms of the optimal policy with CARA utility function. And we conduct Monte Carlo simulation and perform a sensitivity analysis of the optimal asset allocation strategies and the terminal expected utility.
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References
Bo, L. J., Wang, Y. J., & Yang, X. W. (2010). Markov-modulated jump-diffusions for currency option pricing. Insurance: Mathematics and Economics, 46, 461–469.
Davis, M. H. A. (1993). Markov model and optimization. London: Chapman and Hall.
Elliott, R. J., Chan, L., & Siu, T. K. (2005). Option pricing and Esscher transform under regime switching. Annal of Finance, 1, 423–432.
Elliott, R. J., & Osakwe, C. J. (2006). Option pricing for pure jump processes with Markov switching compensators. Finance and Stochastics, 10, 250–275.
Elliott, R. J., Siu, T. K., Chan, L., & Lau, J. W. (2007). Pricing options under a generalized Markov modulated jump diffusion model. Stochastic Analysis and Applications, 25, 821–843.
Elliott, R. J., & Siu, T. K. (2011). Utility-based indifference pricing in regime-switching models. Nonlinear Analysis, 74, 6302–6313.
Kung, J. (2012). A two-asset stochastic model for long-term portfolio selection. Mathematics and Computers in Simulation, 79, 3089–3098.
Li, Z., Zeng, Y., & Lai, Y. (2012). Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model. Insurance: Mathematics and Economics, 51, 191–203.
Merton, R. C. (1971). Optimum consumption and portfolio rules in a continuous-time model. Journal of Economical Theory, 3, 373–413.
Noh, E. J., & Kim, J. H. (2011). An optimal portfolio model with stochastic volatility and stochastic interest rate. Journal of Mathematical Analysis and Apllications, 2, 510–522.
Rieder, U., & Bauerle, N. (2005). Portfolio optimization with unobservable Markov-modulated drift process. Journal of Applied Probability, 42, 362–378.
Shen, Y., & Siu, T. K. (2012). Asset allocation under stochastic interest rate with regime switching. Economic Modelling, 29, 1126–1136.
Siu, T. K., Yang, H. L., & Lau, J. W. (2008). Pricing currency options under two-factor Markov-modulated stochastic volatility models. Insurance: Mathematics and Economics, 43, 295–302.
Yang, H., & Zhang, L. (2005). Optimal invertment for insurer with jump-diffusion risk process. Insurance: Mathematics and Economics, 37, 615–634.
Zariphopoulou, T. (2001). A solution approach to valuation with unhedgeable risks. Finance and Stochastics, 5, 61–82.
Acknowledgments
The authors would like to thank the referee for many helpful and valuable comments and suggestions. This research is supported by “the Fundamental Research Funds for the Central Universities (No: 2014MDLXYXJ01)”. Liu is supported by the Ministry of education of Humanities and Social Sciences project (No:11YJC790102).
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Li, J., Liu, H. Optimal Investment for the Insurers in Markov-Modulated Jump-Diffusion Models. Comput Econ 46, 143–156 (2015). https://doi.org/10.1007/s10614-014-9454-7
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DOI: https://doi.org/10.1007/s10614-014-9454-7