Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers
AbstractFollowing the framework of Promislow and Young (2005), this paper considers an optimal investment–reinsurance problem of an insurer facing a claim process modeled by a Brownian motion with drift under the Markowitz mean–variance criterion. The market modes are divided into a finite number of regimes. All the key parameters change according to the value of different market modes. The insurer chooses to purchase proportional reinsurance to reduce the underlying risk. In addition to reinsurance, we suppose that the insurer is allowed to invest its surplus in a financial market consisting of a risk-free asset (bond or bank account) and a risky asset whose price process is modeled by a geometric Brownian motion. We investigate the feasibility of the problem, obtain an analytic expression for the optimal strategy, delineate the efficient frontier and demonstrate our results with numerical examples.
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Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 53 (2013)
Issue (Month): 3 ()
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Web page: http://www.elsevier.com/locate/inca/505554
Proportional reinsurance; Optimal investment–reinsurance; Geometric Brownian motion; Mean–variance; Efficient frontier;
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- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, Econometric Society, vol. 57(2), pages 357-84, March.
- Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 40(2), pages 267-282, March.
- Chen, Ping & Yang, Hailiang & Yin, George, 2008. "Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 43(3), pages 456-465, December.
- Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262112388, December.
- Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 92(2), pages 307-28, April.
- Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 49(2), pages 207-215, September.
- Guidolin, Massimo & Timmermann, Allan, 2007.
"Asset allocation under multivariate regime switching,"
Journal of Economic Dynamics and Control, Elsevier,
Elsevier, vol. 31(11), pages 3503-3544, November.
- Massimo Guidolin & Allan Timmerman, 2006. "Asset allocation under multivariate regime switching," Working Papers, Federal Reserve Bank of St. Louis 2005-002, Federal Reserve Bank of St. Louis.
- Cao, Yusong & Wan, Nianqing, 2009. "Optimal proportional reinsurance and investment based on Hamilton-Jacobi-Bellman equation," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(2), pages 157-162, October.
- Chen, Shumin & Li, Zhongfei & Li, Kemian, 2010. "Optimal investment-reinsurance policy for an insurance company with VaR constraint," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 47(2), pages 144-153, October.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, American Finance Association, vol. 7(1), pages 77-91, 03.
- Paul Storer & Marc A. Van Audenrode, 1995. "Unemployment Insurance Take-Up Rates in Canada: Facts, Determinants, and Implications," Canadian Journal of Economics, Canadian Economics Association, Canadian Economics Association, vol. 28(4a), pages 822-35, November.
- Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 49(1), pages 145-154, July.
- Zhang, Xin & Siu, Tak Kuen, 2009. "Optimal investment and reinsurance of an insurer with model uncertainty," Insurance: Mathematics and Economics, Elsevier, Elsevier, vol. 45(1), pages 81-88, August.
- Yuping Liu & Jin Ma, 2009. "Optimal reinsurance/investment problems for general insurance models," Papers, arXiv.org 0908.4538, arXiv.org.
- Duan Li & Wan-Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean-Variance Formulation," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(3), pages 387-406.
- Robert Elliott & Tak Kuen Siu, 2009. "On Markov-modulated Exponential-affine Bond Price Formulae," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 16(1), pages 1-15.
- Raymond, Jennie E & Rich, Robert W, 1997. "Oil and the Macroeconomy: A Markov State-Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 29(2), pages 193-213, May.
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