Mean-variance Optimal Reinsurance-investment Strategy in Continuous Time

Daheng Peng; Fang Zhang; Daheng Peng; Fang Zhang

doi:10.3934/QFE.2017.3.320

Quantitative Finance and Economics

2017, Volume 1, Issue 3: 320-333. doi: 10.3934/QFE.2017.3.320

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Research article

Mean-variance Optimal Reinsurance-investment Strategy in Continuous Time

Daheng Peng ^,,
Fang Zhang

School of Finance, Guangdong University of Business Studies, Guangzhou 510320, China

Received: 29 June 2017 Accepted: 19 September 2017 Published: 12 October 2017

In this paper, Lagrange method is used to solve the continuous-time mean-variance reinsurance-investment problem. Proportional reinsurance, multiple risky assets and risk-free asset are considered synthetically in the optimal strategy for insurers. By solving the backward stochastic differential equation for the Lagrange multiplier, we get the mean-variance optimal reinsurance-investment strategy and its effective frontier in explicit forms.

Keywords:

Citation: Daheng Peng, Fang Zhang. Mean-variance Optimal Reinsurance-investment Strategy in Continuous Time[J]. Quantitative Finance and Economics, 2017, 1(3): 320-333. doi: 10.3934/QFE.2017.3.320

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Abstract

References

[1]	Bai L, Guo J (2008) Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint. Insurance: Math and Econ 42: 968–975. doi: 10.1016/j.insmatheco.2007.11.002
[2]	Browne S (1995) Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin. Math Oper Res 20: 937–958. doi: 10.1287/moor.20.4.937
[3]	Cao Y, Wan N (2009) Optimal proportional reinsurance and investment based on Hamilton- Jacobi-Bellman equation. Insurance: Math and Econ 45: 157–162. doi: 10.1016/j.insmatheco.2009.05.006
[4]	Chen P, Yam SCP (2013) Optimal proportional reinsurance and investment with regime-switching for mean-variance insurers . Insurance: Math and Econ 53: 871-883. doi: 10.1016/j.insmatheco.2013.10.004
[5]	Chow G (1999) Duplicating contingent claims by the Lagrange method. Econ Rev 4: 277–283.
[6]	Chow G (1997) Dynamics economics: optimization by the Lagrange method. New York, Oxford Univ Press.
[7]	Chow G (1996) The Lagrange method of optimization with applications to portfolio and investment decisions. J Econ Control 20: 1–18. doi: 10.1016/0165-1889(94)00841-9
[8]	Lim A, Zhou X (2002) Mean-variance portfolio selection with random parameters in a complete market. Math Oper Res 27: 101–120. doi: 10.1287/moor.27.1.101.337
[9]	Luenberger DG (1968) Optimization by vector space methods. Wiley, New York.
[10]	Luo S, Taksar M, Tsoi A (2008) On reinsurance and investment for large insurance portfolios. Insurance: Math Econ 42: 434–444. doi: 10.1016/j.insmatheco.2007.04.002
[11]	Promislow DS, Young VR (2005) Minimizing the probability of ruin when claims follow Brownian motion with drift. North Am Actuar J 9: 109–128. doi: 10.1080/10920277.2005.10596229
[12]	Shen Y, Zeng Y (2015) Optimal investment-reinsurance strategy for mean-variance insurers with square-root factor process. Insurance: Math and Econ 62: 118-137. doi: 10.1016/j.insmatheco.2015.03.009
[13]	Taksar M, Markussen C (2003) Optimal dynamic reinsurance policies for large insurance portfolios. Financ Stoch 7: 97–121. doi: 10.1007/s007800200073
[14]	Yong JM, Zhou XY(1999) Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer Press, New York.
[15]	Zhang X, Zhang K, Yu X (2009) Optimal proportional reinsurance and investment with transaction costs, I: Maximizing the terminal wealth. Insurance: Math Econ 44: 473–478.
[16]	Zhou X, Li D (2000) Continuous-time mean-variance portfolio selection: A stochastic LQ framework. Appl Math Optim 42: 19–33. doi: 10.1007/s002450010003

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