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Equilibrium Policy on Dividend and Capital Injection under Time-inconsistent Preferences

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  • Sang Hu
  • Zihan Zhou

Abstract

This paper studies the dividend and capital injection problem under a diffusion risk model with general discount functions. A proportional cost is imposed when injecting capitals. For exponential discounting as time-consistent benchmark, we obtain the closed-form solutions and show that the optimal strategies are of threshold type. Under general discount function which leads to time-inconsistency, we adopt the definition of weak equilibrium and obtain the extended HJB equation system. An explicit solution is derived under pseudo-exponential discounting where three cases of the dividend and capital injection thresholds are obtained. Numerical examples show that large capital injection cost may lead to no capital injection at all, while larger difference in group discount rate leads to higher equilibrium value function.

Suggested Citation

  • Sang Hu & Zihan Zhou, 2025. "Equilibrium Policy on Dividend and Capital Injection under Time-inconsistent Preferences," Papers 2505.23511, arXiv.org.
    • Handle: RePEc:arx:papers:2505.23511
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    References listed on IDEAS

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    1. Chen, Shumin & Li, Zhongfei & Zeng, Yan, 2014. "Optimal dividend strategies with time-inconsistent preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 150-172.
    2. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2012. "Time-Inconsistent Stochastic Linear--Quadratic Control," Post-Print hal-00691816, HAL.
    3. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    4. He, Lin & Liang, Zongxia, 2008. "Optimal financing and dividend control of the insurance company with proportional reinsurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 976-983, June.
    5. Chen, Shumin & Wang, Xi & Deng, Yinglu & Zeng, Yan, 2016. "Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 27-37.
    6. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 49-74, May.
    7. Yongwu Li & Zhongfei Li & Yan Zeng, 2016. "Equilibrium Dividend Strategy with Non-exponential Discounting in a Dual Model," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 699-722, February.
    8. Zhao, Qian & Wei, Jiaqin & Wang, Rongming, 2014. "On dividend strategies with non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 1-13.
    9. Løkka, Arne & Zervos, Mihail, 2008. "Optimal dividend and issuance of equity policies in the presence of proportional costs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 954-961, June.
    10. Suresh P. Sethi & Michael I. Taksar, 2002. "Optimal Financing of a Corporation Subject To Random Returns," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 155-172, April.
    11. Avanzi, Benjamin & Shen, Jonathan & Wong, Bernard, 2011. "Optimal Dividends and Capital Injections in the Dual Model with Diffusion," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 611-644, November.
    12. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    13. Ebert, Sebastian & Wei, Wei & Zhou, Xun Yu, 2020. "Weighted discounting—On group diversity, time-inconsistency, and consequences for investment," Journal of Economic Theory, Elsevier, vol. 189(C).
    14. Chen, Shumin & Zeng, Yan & Hao, Zhifeng, 2017. "Optimal dividend strategies with time-inconsistent preferences and transaction costs in the Cramér–Lundberg model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 31-45.
    15. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 270-278, October.
    16. Bjarne Hø Jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182, April.
    17. Zhou, Ming & Yuen, Kam C., 2012. "Optimal reinsurance and dividend for a diffusion model with capital injection: Variance premium principle," Economic Modelling, Elsevier, vol. 29(2), pages 198-207.
    18. Tomas Björk & Agatha Murgoci & Xun Yu Zhou, 2014. "Mean–Variance Portfolio Optimization With State-Dependent Risk Aversion," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 1-24, January.
    19. He, Xuedong & Hu, Sang, 2024. "Never stop or never start? Optimal stopping under a mixture of CPT and EUT preferences," Journal of Economic Theory, Elsevier, vol. 222(C).
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