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Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity

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  • Guan, Guohui
  • Hu, Xiang

Abstract

This work investigates the equilibrium investment and reinsurance strategies for a general insurance company under smooth ambiguity. The general insurance company holds shares of an insurance company and a reinsurance company. The claims of the insurer follow a compound Poisson process. The insurer can divide part of the insurance risk to the reinsurer. Besides, the insurer and reinsurer both participate in the financial market and invest in cash and stock. However, the general insurance company is ambiguous about the insurance and financial risks and is an ambiguity-averse manager (AAM). The uncertainties over the insurance and financial risks are described by second-order distributions. The AAM aims to maximize the average performance of the weighted sum surplus process of the insurer and reinsurer under the mean–variance criterion and smooth ambiguity. We present the extended Hamilton–Jacobi–Bellman (HJB) system for the optimization problem combining the mean–variance criterion and smooth ambiguity. In the case that the second-order distributions are Gaussian, we obtain the closed-forms of the equilibrium reinsurance and investment strategies. At the end of this work, sensitivity analyses are presented to show the economic behaviors of the AAM.

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  • Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    • Handle: RePEc:eee:ecofin:v:63:y:2022:i:c:s1062940822001310
    DOI: 10.1016/j.najef.2022.101793
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    1. Cai, Jun & Lemieux, Christiane & Liu, Fangda, 2016. "Optimal Reinsurance From The Perspectives Of Both An Insurer And A Reinsurer," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 815-849, September.
    2. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    3. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    4. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.
    5. Xin Zhang & Ming Zhou & Junyi Guo, 2007. "Optimal combinational quota‐share and excess‐of‐loss reinsurance policies in a dynamic setting," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(1), pages 63-71, January.
    6. Tomas Björk & Agatha Murgoci, 2014. "A theory of Markovian time-inconsistent stochastic control in discrete time," Finance and Stochastics, Springer, vol. 18(3), pages 545-592, July.
    7. Gu, Ailing & Viens, Frederi G. & Yao, Haixiang, 2018. "Optimal robust reinsurance-investment strategies for insurers with mean reversion and mispricing," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 93-109.
    8. Yuping Liu & Jin Ma, 2009. "Optimal reinsurance/investment problems for general insurance models," Papers 0908.4538, arXiv.org.
    9. Nengjiu Ju & Jianjun Miao, 2012. "Ambiguity, Learning, and Asset Returns," Econometrica, Econometric Society, vol. 80(2), pages 559-591, March.
    10. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    11. Zhibin Liang & Kam Chuen Yuen & Ka Chun Cheung, 2012. "Optimal reinsurance–investment problem in a constant elasticity of variance stock market for jump‐diffusion risk model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 28(6), pages 585-597, November.
    12. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    13. Daniel Lacker & Thaleia Zariphopoulou, 2019. "Mean field and n‐agent games for optimal investment under relative performance criteria," Mathematical Finance, Wiley Blackwell, vol. 29(4), pages 1003-1038, October.
    14. Matteo Brachetta & Hanspeter Schmidli, 2020. "Optimal reinsurance and investment in a diffusion model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 341-361, June.
    15. Lorenzo Garlappi & Raman Uppal & Tan Wang, 2007. "Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach," The Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 41-81, January.
    16. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    17. Liu, Bing & Meng, Hui & Zhou, Ming, 2021. "Optimal investment and reinsurance policies for an insurer with ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    18. Jaroslav Borovička, 2020. "Survival and Long-Run Dynamics with Heterogeneous Beliefs under Recursive Preferences," Journal of Political Economy, University of Chicago Press, vol. 128(1), pages 206-251.
    19. Jieming Zhou & Xiangqun Yang & Ya Huang, 2017. "Robust optimal investment and proportional reinsurance toward joint interests of the insurer and the reinsurer," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10733-10757, November.
    20. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    21. Costis Skiadas, 2013. "Smooth Ambiguity Aversion toward Small Risks and Continuous-Time Recursive Utility," Journal of Political Economy, University of Chicago Press, vol. 121(4), pages 000.
    22. Hainaut, Donatien, 2017. "Contagion modeling between the financial and insurance markets with time changed processes," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 63-77.
    23. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    24. Hainaut, Donatien, 2017. "Contagion modeling between the financial and insurance markets with time changed processes," LIDAM Reprints ISBA 2017016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    25. Ceci, Claudia & Colaneri, Katia & Cretarola, Alessandra, 2022. "Optimal reinsurance and investment under common shock dependence between financial and actuarial markets," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 252-278.
    26. Borch, Karl, 1960. "Reciprocal Reinsurance Treaties," ASTIN Bulletin, Cambridge University Press, vol. 1(4), pages 170-191, December.
    27. Guan, Guohui & Liang, Zongxia & Feng, Jian, 2018. "Time-consistent proportional reinsurance and investment strategies under ambiguous environment," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 122-133.
    28. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    29. Zhang, Caibin & Liang, Zhibin, 2022. "Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    30. Yi, Bo & Li, Zhongfei & Viens, Frederi G. & Zeng, Yan, 2013. "Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 601-614.
    31. Borch, Karl, 1969. "The optimal reinsurance treaty," ASTIN Bulletin, Cambridge University Press, vol. 5(2), pages 293-297, May.
    32. Brachetta, M. & Ceci, C., 2019. "Optimal proportional reinsurance and investment for stochastic factor models," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 15-33.
    33. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    34. Ambrose Lo & Zhaofeng Tang, 2019. "Pareto-optimal reinsurance policies in the presence of individual risk constraints," Annals of Operations Research, Springer, vol. 274(1), pages 395-423, March.
    35. Peng Yang & Zhiping Chen & Liyuan Wang, 2021. "Time-consistent reinsurance and investment strategy combining quota-share and excess of loss for mean-variance insurers with jump-diffusion price process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(11), pages 2546-2568, June.
    36. Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
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    More about this item

    Keywords

    Proportional reinsurance; Investment; Equilibrium strategy; Smooth ambiguity; Mean–variance;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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