
AIMS Mathematics, 2020, 5(6): 69967013. doi: 10.3934/math.2020449
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Equilibrium investment and risk control for an insurer with nonMarkovian regimeswitching and noshorting 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
Received: , Accepted: , Published:
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, Meanvariance portfolio optimization with statedependent risk aversion, Math. Financ., 24 (2014), 124.
3. P. Chen, H. Yang, Markowitz's meanvariance assetliability management with regime switching: A multiperiod model, Appl. Math. Finance, 18 (2011), 2950.
4. P. Chen, H. Yang, G. Yin, Markowitz's meanvariance assetliability management with regime switching: A continuoustime model, Insur. Math. Econ., 43 (2008), 456465.
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, Timeinconsistent stochastic linearquadratic control, SIAM J. Control Optim., 50 (2012), 15481572.
8. Y. Hu, J. Huang, X. Li, Equilibrium for timeinconsistent stochastic linearquadratic control under constraint, arXiv preprint arXiv:1703.09415, 2017.
9. Y. Hu, H. Jin, X.Y. Zhou, Timeinconsistent stochastic linearquadratic control: Characterization and uniqueness of equilibrium, SIAM J. Control Optim., 55 (2017), 12611279.
10. N. Kazamaki, Continuous Exponential Martingales and BMO, Berlin: Springer, 1994.
11. H. Markowitz, Portfolio selection, J. Finance, 7 (1952), 7791.
12. Y. Shen, J. Wei, Q. Zhao, Meanvariance assetliability management problem under nonMarkovian regimeswitching models, Appl. Math. Opt., 81 (2020), 859897.
13. Z. Sun, J. Guo, Optimal meanvariance investment and reinsurance problem for an insurer with stochastic volatility, Math. Method. Oper. Res., 88 (2018), 5979.
14. Z. Sun, X. Guo, Equilibrium for a timeinconsistent stochastic linearquadratic control system with jumps and its application to the meanvariance problem, J. Optimiz. Theory App., 181 (2019), 383410.
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 noshort selling, J. Comput. Appl. Math., 366 (2020), 112413.
16. Z. Sun, X. Zhang, K. C. Yuen, Meanvariance assetliability management with affine diffusion factor process and a reinsurance option, Scand. Actuar. J., 2020 (2020), 218244.
17. Y. Tian, J. Guo, Z. Sun, Optimal meanvariance 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, Meanvariance portfolio selection under a nonMarkovian regimeswitching model, J. Comput. Appl. Math., 350 (2019), 442455.
19. T. Wang, Z. Jin, J. Wei, Meanvariance portfolio selection under a nonMarkovian regimeswitching model: Timeconsistent solutions, SIAM J. Control Optim., 57 (2019), 32493271.
20. J. Wei, K. C. Wong, S. C. P. Yam, et al. Markowitz's meanvariance assetliability management with regime switching: A timeconsistent approach, Insur. Math. Econ., 53 (2013), 281291.
21. J. Wei, T. Wang, Timeconsistent meanvariance assetliability management with random coefficients, Insur. Math. Econ., 77 (2017), 8496.
22. Y. Zeng, Z. Li, Optimal timeconsistent investment and reinsurance policies for meanvariance insurers, Insur. Math. Econ., 49 (2011), 145154.
23. L. Zhang, R. Wang, J. Wei, Optimal meanvariance reinsurance and investment strategy with constraints in a nonMarkovian regimeswitching model, Stat. Theory Related Fields., doi: 10.1080/24754269.2020.1719356, 2020.
24. H. Zhao, Y. Shen, Y. Zeng, Timeconsistent investmentreinsurance strategy for meanvariance insurers with a defaultable security, J. Math. Anal. Appl., 437 (2016), 10361057.
25. X. Y. Zhou, G. Yin, Markowitz's meanvariance portfolio selection with regime switching: A continuoustime model, SIAM J. Control Optim., 42 (2003), 14661482.
26. B. Zou, A. Cadenillas, Optimal investment and risk control policies for an insurer: Expected utility maximization, Insur. Math. Econ., 58 (2014), 5767.
© 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)