AIMS Mathematics, 2020, 5(6): 6996-7013. doi: 10.3934/math.2020449

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Equilibrium investment and risk control for an insurer with non-Markovian regime-switching and no-shorting constraints

1 College of Transportation, Shandong University of Science and Technology, Qingdao, Shandong 266590, China
2 School of Statistics, Qufu Normal University, Qufu, Shandong 273165, China
3 School of Business, Hunan Normal University, Changsha, Hunan 410081, China

In this paper, we study the time-consistent equilibrium investment and risk control policies for an insurer under the mean-variance criterion. The dynamics of liability and assets are given by non-Markovian regime-switching models driven by a Brownian motion and a continuous time finite-state Markov chain. It is assumed that the insurer has a time-varying preference of risk depending dynamically on current wealth, and is not allowed to short sell the risky assets. With the aid of backward stochastic differential equations and bounded mean oscillation martingales, we obtain feedback representations of the open-loop equilibrium strategies. Finally, the result is also applied to solve an example of the Markovian regime-switching model.
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References

1. T. Björk, A. Murgoci, A General Theory of Markovian Time Inconsistent Stochastic Control Problems, SSRN Electronic Journal, 2010.

2. T. Björk, A. Murgoci, X. Y. Zhou, Mean-variance portfolio optimization with state-dependent risk aversion, Math. Financ., 24 (2014), 1-24.    

3. P. Chen, H. Yang, Markowitz's mean-variance asset-liability management with regime switching: A multi-period model, Appl. Math. Finance, 18 (2011), 29-50.    

4. P. Chen, H. Yang, G. Yin, Markowitz's mean-variance asset-liability management with regime switching: A continuous-time model, Insur. Math. Econ., 43 (2008), 456-465.    

5. R. J. Elliott, L. Aggoun, J. B. Moore, Hidden Markov Models: Estimation and Control, Springer Science & Business Media, 1995.

6. J. Grandell, Aspects of Risk Theory, New York : Springer, 1991.

7. Y. Hu, H. Jin, X.Y. Zhou, Time-inconsistent stochastic linear-quadratic control, SIAM J. Control Optim., 50 (2012), 1548-1572.    

8. Y. Hu, J. Huang, X. Li, Equilibrium for time-inconsistent stochastic linear-quadratic control under constraint, arXiv preprint arXiv:1703.09415, 2017.

9. Y. Hu, H. Jin, X.Y. Zhou, Time-inconsistent stochastic linear-quadratic control: Characterization and uniqueness of equilibrium, SIAM J. Control Optim., 55 (2017), 1261-1279.    

10. N. Kazamaki, Continuous Exponential Martingales and BMO, Berlin: Springer, 1994.

11. H. Markowitz, Portfolio selection, J. Finance, 7 (1952), 77-91.

12. Y. Shen, J. Wei, Q. Zhao, Mean-variance asset-liability management problem under nonMarkovian regime-switching models, Appl. Math. Opt., 81 (2020), 859-897.    

13. Z. Sun, J. Guo, Optimal mean-variance investment and reinsurance problem for an insurer with stochastic volatility, Math. Method. Oper. Res., 88 (2018), 59-79.    

14. Z. Sun, X. Guo, Equilibrium for a time-inconsistent stochastic linear-quadratic control system with jumps and its application to the mean-variance problem, J. Optimiz. Theory App., 181 (2019), 383-410.    

15. Z. Sun, K. C. Yuen, J. Guo, A BSDE approach to a class of dependent risk model of meanvariance insurers with stochastic volatility and no-short selling, J. Comput. Appl. Math., 366 (2020), 112413.

16. Z. Sun, X. Zhang, K. C. Yuen, Mean-variance asset-liability management with affine diffusion factor process and a reinsurance option, Scand. Actuar. J., 2020 (2020), 218-244.    

17. Y. Tian, J. Guo, Z. Sun, Optimal mean-variance reinsurance in a financial market with stochastic rate of return, J. Ind. Manag. Optim., doi: 10.3934/jimo.2020051, 2020.

18. T. Wang, J. Wei, Mean-variance portfolio selection under a non-Markovian regime-switching model, J. Comput. Appl. Math., 350 (2019), 442-455.    

19. T. Wang, Z. Jin, J. Wei, Mean-variance portfolio selection under a non-Markovian regimeswitching model: Time-consistent solutions, SIAM J. Control Optim., 57 (2019), 3249-3271.    

20. J. Wei, K. C. Wong, S. C. P. Yam, et al. Markowitz's mean-variance asset-liability management with regime switching: A time-consistent approach, Insur. Math. Econ., 53 (2013), 281-291.    

21. J. Wei, T. Wang, Time-consistent mean-variance asset-liability management with random coefficients, Insur. Math. Econ., 77 (2017), 84-96.    

22. Y. Zeng, Z. Li, Optimal time-consistent investment and reinsurance policies for mean-variance insurers, Insur. Math. Econ., 49 (2011), 145-154.    

23. L. Zhang, R. Wang, J. Wei, Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model, Stat. Theory Related Fields., doi: 10.1080/24754269.2020.1719356, 2020.

24. H. Zhao, Y. Shen, Y. Zeng, Time-consistent investment-reinsurance strategy for mean-variance insurers with a defaultable security, J. Math. Anal. Appl., 437 (2016), 1036-1057.    

25. X. Y. Zhou, G. Yin, Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim., 42 (2003), 1466-1482.    

26. B. Zou, A. Cadenillas, Optimal investment and risk control policies for an insurer: Expected utility maximization, Insur. Math. Econ., 58 (2014), 57-67.    

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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