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Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rate

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  • Zailei Cheng

Abstract

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual risk model, under a stochastic interest rate, assuming the discounting factor follows a geometric Brownian motion or exponential L\'evy process. We will show that closed form solutions can be obtained.

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  • Zailei Cheng, 2017. "Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rate," Papers 1705.08411, arXiv.org.
    • Handle: RePEc:arx:papers:1705.08411
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    References listed on IDEAS

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    1. Eisenberg, Julia, 2015. "Optimal dividends under a stochastic interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 259-266.
    2. Julia Eisenberg & Paul Kruhner, 2016. "A Note on the Optimal Dividends Paid in a Foreign Currency," Papers 1603.07615, arXiv.org.
    3. Arash Fahim & Lingjiong Zhu, 2016. "Asymptotic Analysis for Optimal Dividends in a Dual Risk Model," Papers 1601.03435, arXiv.org, revised Dec 2022.
    4. Hans Gerber & Elias Shiu, 2006. "On Optimal Dividend Strategies In The Compound Poisson Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 76-93.
    5. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, July.
    6. 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.
    7. Peng, Dan & Liu, Donghai & Liu, Zaiming, 2013. "Dividend problems in the dual risk model with exponentially distributed observation time," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 841-849.
    8. Cheung, Eric C.K. & Drekic, Steve, 2008. "Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 399-422, November.
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    Cited by:

    1. Elena Bandini & Tiziano De Angelis & Giorgio Ferrari & Fausto Gozzi, 2022. "Optimal dividend payout under stochastic discounting," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 627-677, April.

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