Optimal investment and insurer–reinsurer strategies under a geometric mean-reverting model with taxation and dividend effects
Optimal Investment and Insurer–Reinsurer
Keywords:
Geometric mean reversion (GMR), Optimal investment, Reinsurance, Federal income tax, Dividend yield, Hamilton–Jacobi–Bellman equationAbstract
Insurance and reinsurance companies play a vital role in modern financial markets worldwide, including developing insurance markets such as Tanzania. Most studies look at optimal investment and reinsurance choices from the insurer’s point of view. However, these strategies might not serve the reinsurer’s interests. This study fills that gap by exploring investment and reinsurance strategies that consider both parties’ interests using a Geometric Mean-Reverting (GMR) model with dividend payments and federal income tax. Both parties invest in a risk-free asset and in-dependent risky assets, whose prices follow mean-reverting patterns. We formulate the problem as a stochastic control problem. The goal is to maximize the expected product of exponential terminal wealth utilities for both parties. By applying Hamilton–Jacobi–Bellman equations, we derive explicit optimal strategies for investment and reinsurance. The results show that the optimal reinsurance strategy is independent of the financial market parameters associated with the risky assets, including the mean-reversion, volatility, dividend, and tax parameters. Instead, it is determined by insurance and reinsurance characteristics such as safety-loadings, claim-risk parameters, and risk-aversion preferences. In contrast, the optimal investment strategies differ between the insurer and the reinsurer because of their distinct risk preferences and financial structures. Taxation significantly affects investment behavior, with lower tax rates encouraging greater investment in risky assets and consequently increasing expected returns and dividend income. Numerical experiments further illustrate the sensitivity of the optimal strategies to key model parameters. These findings emphasize the need to consider joint decision-making, mean-reverting dynamics, taxation, and dividend policies when modeling insurance and reinsurance strategies. They offer a practical approach for optimizing financial decisions in today’s insurance markets.
Downloads
References
Agliardi, E., Charalambides, M., & Koussis, N. (2024). Earnings mean reversion and dynamic optimal capital structure. Quantitative Finance, 24 (7), 993–1015. https://doi.org/10.1080/14697688.2024.2361018
Almeida, H., Campello, M., Laranjeira, B., & Weisbenner, S. (2020). Corporate debt maturity and the real effects of the 2007 credit crisis. Critical Finance Review, 9 (1), 3–58. https://doi.org/10.1561/104.00000044
Borch, K. (1960). The safety loading of reinsurance premiums. Scandinavian Actuarial Journal, 43, 163–184. https://doi.org/10.1080/03461238.1960.10404766
Cai, J., Fang, Y., & Li, Z. (2013). Optimal reinsurance strategies under joint survival probability. ASTIN Bulletin, 43 (2), 503–530. https://doi.org/10.1017/asb.2013.10
Ceci, C., & Colaneri, K. (2025). Portfolio and reinsurance optimization under unknown market price of risk. Quantitative Finance, 25 (2), 217–229. https://doi.org/10.1080/14697688.2024.2384392
Colaneri, K., Cretarola, A., & Salterini, B. (2021). Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences. Mathematics, 9 (14), 1610. https://doi.org/10.3390/math9141610
Consigli, G., Dentcheva, D., Maggioni, F., & Micheli, G. (2026). Asset liability management under sequential stochastic dominance constraints. Annals of Operations Research, 1–42. https://doi.org/10.1007/s10479-025-06988-9
Cox, J. C. (1975). Notes on option pricing i: Constant elasticity of variance diffusions (Working Paper). Stanford University.
Dias, M. A. G. (1996). Valuation of exploration and production assets: An overview of real options models. SPE Annual Technical Conference. https://doi.org/10.2118/35985-MS
Dimitrova, D. S. (2010). Optimal reinsurance under joint survival probability. Insurance: Mathematics and Economics, 47 (3), 324–329. https://doi.org/10.1016/j.insmatheco.2010.07.004
Dixit, A. K., & Pindyck, R. S. (1994). Investment under uncertainty. Princeton University Press. https://doi.org/10.1515/9781400830176
Fama, E. F., & French, K. R. (2001). Disappearing dividends: Changing firm characteristics or lower propensity to pay? Journal of Financial Economics, 60 (1), 3–43. https://doi.org/10.1016/S0304-405X(01)00038-1
Fang, Y., & Li, Z. (2014). Optimal reinsurance strategies with joint interests. Insurance: Mathematics and Economics, 55, 95–104. https://doi.org/10.1016/j.insmatheco.2014.01.006
Feldblum, S. (2007). Taxation of property-casualty insurance companies. Casualty Actuarial Society Forum, 1–50. Available from the Casualty Actuarial Society (CAS) online publications/study-note archive.
Fjeldstad, O.-H. (2020). Tax policy responses to covid-19 in developing countries (tech. rep. No. 122). ICTD. https://doi.org/10.2139/ssrn.3681384
Fleming, W. H., & Soner, H. M. (2006). Controlled markov processes and viscosity solutions. Springer. https://doi.org/10.1007/0-387-31071-1_2
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6 (2), 327–343. https://doi.org/10.1093/rfs/6.2.327
Hogg, R. V. (1959). On the taxation of life insurance companies. Journal of Risk and Insurance, 26 (3), 413–421. Available through the Journal of Risk and Insurance archives and academic library databases.
Huang, Y., & Yang, H. (2018). Robust optimal investment and reinsurance strategies under model uncertainty. Insurance: Mathematics and Economics, 80, 1–10. https://doi.org/10.1016/j.insmatheco.2018.01.002
Huang, Y., Yu, W., Pan, Y., & Cui, C. (2019). Estimating the gerber-shiu expected discounted penalty function for l´evy risk model. Discrete Dynamics in Nature and Society, 2019, https://doi.org/10.1155/ 2019/3607201
Huber, A. (2024). Stochastic modelling in the asset-liability management of life insurance companies–a scenario-based approach for interest rate risk management [Doctoral dissertation, Technische Universit¨at Wien]. https://doi.org/10.34726/hss.2024.110668
Kaishev, V. K. (2004). Optimal reinsurance under joint survival probability maximization. Insurance: Mathematics and Economics, 34 (3), 375–400. https://doi.org/10.1016/j.insmatheco.2003.12.004
Launie, J. J. (1971). Tax incidence in life insurance companies: An empirical analysis. Journal of Risk and Insurance, 38 (3), 409–422. Available through the Journal of Risk and Insurance archives and academic library databases.
Li, D., & Shen, Y. (2014). Optimal investment and reinsurance strategies under exponential utility. Insurance: Mathematics and Economics, 56, 1–12. https://doi.org/10.1016/j.insmatheco.2014.02.005
Li, D., Zeng, Y., & Yang, H. (2018). Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps. Scandinavian Actuarial Journal, 145–171. https://doi.org/10.1080/03461238.2017.1309679
Li, Y., Mao, X., Song, Y., & Tao, J. (2022). Optimal investment and proportional reinsurance strategy under the mean-reverting ornstein-uhlenbeck process and net profit condition. Journal of Industrial and Management Optimization, 18 (1), 75–93. https://doi.org/10.3934/jimo.2020143
Lintner, J. (1956). Distribution of incomes of corporations among dividends, retained earnings, and taxes. American Economic Review, 46 (2), 97–113. https://www.jstor.org/stable/1910664
Mbigili, L. J. (2012). Optimal portfolio management when stocks are driven by mean-reverting processes [Doctoral dissertation, University of Dar es Salaam]. Available from the University of Dar es Salaam Library Repository.
Miller, M. H., & Modigliani, F. (1961). Dividend policy, growth, and the valuation of shares. Journal of Business, 34 (4), 411–433. https://doi.org/10.1086/294442
Mwigilwa, W. F., Mhlanga, F. J., & Sinkwembe, E. (2025). Optimal investment and reinsurance strategies with federal income tax under the geometric mean reversion (GMR) model. Journal of Industrial and Management Optimization, 21 (4), 2778–2794. https://doi.org/10.3934/jimo.2024193
Oksendal, B. (2013). Stochastic differential equations: An introduction with ap-plications. Springer Science & Business Media. https://doi.org/10.1007/978-3-662-03620-4
Peng, X., Su, W., & Zhang, Z. (2020). On a perturbed compound poisson risk model under a periodic threshold-type dividend strategy. Journal of Industrial and Management Optimization, 16. https://doi.org/10.3934/jimo.2019038
Sarkar, S. (2000). On the investment–uncertainty relationship in a real options model. Journal of Economic Dynamics and Control, 24 (2), 219–225. https://doi.org/10.1016/S0165-1889(99)00014-2
Schwartz, E. S. (1997). The stochastic behavior of commodity prices: Implica-tions for valuation and hedging. Journal of Finance, 52 (3), 923–973. https://doi.org/10.1111/j.1540-6261.1997.tb02721.x
Stein, E. M., & Stein, J. C. (1991). Stock price distributions with stochastic volatility: An analytic approach. Review of Financial Studies, 4 (4), 727–752. https://doi.org/10.1093/rfs/4.4.727
Yu, W., Huang, Y., & Cui, C. (2018). The absolute ruin insurance risk model with a threshold dividend strategy. Symmetry, 10, 377. https://doi.org/10.3390/sym10090377
Zeng, Y., & Li, Z. (2013). Stochastic pareto-optimal reinsurance policies. Insur-ance: Mathematics and Economics, 53 (3), 597–605. https://doi.org/10.1016/j.insmatheco.2013.07.002
Zhang, X., & Li, J. (2023). Optimal reinsurance and investment under hara utility. Applied Mathematics and Computation, 450, 127456. https://doi.org/10.1016/j.amc.2023.127456
Zhang, X., & Zhao, P. (2022). Optimal investment and reinsurance with default-able bonds. European Journal of Operational Research, 300 (2), 789–803. https://doi.org/10.1016/j.ejor.2021.08.021
Downloads
Additional Files
Published
Data Availability Statement
Data sharing not applicable to this article, as no datasets were generated or analysed during the current study
License
Copyright (c) 2026 Winfrida Felix Mwigilwa
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The Creative Commons Attribution-NonCommercial 4.0 (CC BY-NC 4.0) license allows you to use, remix, and build upon a work non-commercially, provided you give proper attribution to the original creator and any new works are not used for commercial purposes. You are free to share and adapt the material, but you cannot use it for a commercial advantage or monetary compensation.
