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Asymptotic Analysis for Optimal Dividends in a Dual Risk Model

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  • Arash Fahim
  • Lingjiong Zhu

Abstract

The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk model. It is well known that the value function of this optimal control problem does not yield closed-form solutions except in some special cases. In this paper, we study the asymptotics of the optimal dividend problem when the parameters of the model go to either zero or infinity. Our results provide insights to the optimal strategies and the optimal values when the parameters are extreme.

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  • Arash Fahim & Lingjiong Zhu, 2016. "Asymptotic Analysis for Optimal Dividends in a Dual Risk Model," Papers 1601.03435, arXiv.org, revised Dec 2022.
    • Handle: RePEc:arx:papers:1601.03435
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    References listed on IDEAS

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    1. Wang, Zengwu & Xia, Jianming & Zhang, Lihong, 2007. "Optimal investment for an insurer: The martingale approach," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 322-334, March.
    2. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    3. Arash Fahim & Lingjiong Zhu, 2015. "Optimal Investment in a Dual Risk Model," Papers 1510.04924, arXiv.org, revised Feb 2023.
    4. Erhan Bayraktar & Masahiko Egami, 2008. "Optimizing venture capital investments in a jump diffusion model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 21-42, February.
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    6. Afonso, Lourdes B. & Cardoso, Rui M.R. & Egídio dos Reis, Alfredo D., 2013. "Dividend problems in the dual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 906-918.
    7. Albrecher, Hansjörg & Badescu, Andrei & Landriault, David, 2008. "On the dual risk model with tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1086-1094, June.
    8. Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org, revised Feb 2023.
    9. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    10. Ng, Andrew C.Y., 2010. "On the Upcrossing and Downcrossing Probabilities of a Dual Risk Model With Phase-Type Gains," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 281-306, May.
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    Cited by:

    1. Zailei Cheng, 2017. "Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rate," Papers 1705.08411, arXiv.org.
    2. Arash Fahim & Lingjiong Zhu, 2023. "Optimal Investment in a Dual Risk Model," Risks, MDPI, vol. 11(2), pages 1-29, February.
    3. Zailei Cheng, 2017. "Optimal dividends in the dual risk model under a stochastic interest rate," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-16, March.

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