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Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks

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  • Guan, Guohui
  • Liang, Zongxia

Abstract

In this paper, we investigate an optimal reinsurance and investment problem for an insurer whose surplus process is approximated by a drifted Brownian motion. Proportional reinsurance is to hedge the risk of insurance. Interest rate risk and inflation risk are considered. We suppose that the instantaneous nominal interest rate follows an Ornstein–Uhlenbeck process, and the inflation index is given by a generalized Fisher equation. To make the market complete, zero-coupon bonds and Treasury Inflation Protected Securities (TIPS) are included in the market. The financial market consists of cash, zero-coupon bond, TIPS and stock. We employ the stochastic dynamic programming to derive the closed-forms of the optimal reinsurance and investment strategies as well as the optimal utility function under the constant relative risk aversion (CRRA) utility maximization. Sensitivity analysis is given to show the economic behavior of the optimal strategies and optimal utility.

Suggested Citation

  • Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:105-115
    DOI: 10.1016/j.insmatheco.2014.01.007
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    Cited by:

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    3. Christian Biener & Martin Eling & Shailee Pradhan, 2015. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2013 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 18(1), pages 129-141, March.
    4. Sheng Delei, 2016. "Explicit Solution of the Optimal Reinsurance-Investment Problem with Promotion Budget," Journal of Systems Science and Information, De Gruyter, vol. 4(2), pages 131-148, April.
    5. Zou, Bin & Cadenillas, Abel, 2014. "Optimal investment and risk control policies for an insurer: Expected utility maximization," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 57-67.
    6. Chang Hao & Wang Chunfeng & Fang Zhenming, 2017. "Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework," Journal of Systems Science and Information, De Gruyter, vol. 5(3), pages 229-249, June.
    7. Peng, Xingchun & Wang, Wenyuan, 2016. "Optimal investment and risk control for an insurer under inside information," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 104-116.
    8. Balbás, Alejandro & Garrido, José & Okhrati, Ramin, 2016. "Good deal measurement in asset pricing: Actuarial and financial implications," INDEM - Working Paper Business Economic Series 23546, Instituto para el Desarrollo Empresarial (INDEM).
    9. Jiaqi Zhu & Shenghong Li, 2020. "Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility," Mathematics, MDPI, vol. 8(12), pages 1-22, December.
    10. Chang, Hao, 2015. "Dynamic mean–variance portfolio selection with liability and stochastic interest rate," Economic Modelling, Elsevier, vol. 51(C), pages 172-182.
    11. Jian Pan & Qingxian Xiao, 2017. "Optimal mean–variance asset-liability management with stochastic interest rates and inflation risks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(3), pages 491-519, June.
    12. Martin Eling & Ruo Jia, 2017. "Recent Research Developments Affecting Nonlife Insurance—The CAS Risk Premium Project 2014 Update," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 20(1), pages 63-77, March.
    13. Ling Wang & Kexin Chen & Mei Choi Chiu & Hoi Ying Wong, 2021. "Optimal Expansion of Business Opportunity," Papers 2112.06706, arXiv.org.
    14. Stanley Jere & Elias R. Offen & Othusitse Basmanebothe, 2022. "Optimal Investment, Consumption and Life Insurance Problem with Stochastic Environments," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(4), pages 1-33, November.
    15. Wang, Ling & Chen, Kexin & Chiu, Mei Choi & Wong, Hoi Ying, 2023. "Optimal expansion of business opportunity," European Journal of Operational Research, Elsevier, vol. 309(1), pages 432-445.
    16. 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.
    17. Liang, Zongxia & Song, Min, 2015. "Time-consistent reinsurance and investment strategies for mean–variance insurer under partial information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 66-76.
    18. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    19. Guan, Guohui & Liang, Zongxia, 2019. "Robust optimal reinsurance and investment strategies for an AAI with multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 63-78.
    20. Guan, Guohui & Liang, Zongxia, 2015. "Mean–variance efficiency of DC pension plan under stochastic interest rate and mean-reverting returns," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 99-109.
    21. Bin Zou & Abel Cadenillas, 2014. "Optimal Investment and Risk Control Problem for an Insurer: Expected Utility Maximization," Papers 1402.3560, arXiv.org, revised Mar 2014.
    22. Esfandi, Elaheh & Mousavi, Mir Hossein & Moshrefi, Rassam & Farhang-Moghaddam, Babak, 2020. "Insurer Optimal Asset Allocation in a Small and Closed Economy: The Case of Iran’s Social Security Organization," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 15(4), pages 445-461, October.
    23. Li, Danping & Rong, Ximin & Zhao, Hui, 2015. "Time-consistent reinsurance–investment strategy for a mean–variance insurer under stochastic interest rate model and inflation risk," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 28-44.
    24. Mei-Ling Tang & Ting-Pin Wu & Ming-Chin Hung, 2022. "Optimal Pension Fund Management with Foreign Investment in a Stochastic Environment," Mathematics, MDPI, vol. 10(14), pages 1-21, July.
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    More about this item

    Keywords

    IE13; IE12; IM52; IB91; IE53; IE43; Optimal proportional reinsurance strategy; Optimal investment strategy; CRRA utility; Stochastic dynamic programming; Stochastic inflation index; Stochastic interest rate;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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