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A State-Dependent Dual Risk Model

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  • Lingjiong Zhu

Abstract

In a dual risk model, the premiums are considered as the costs and the claims are regarded as the profits. The surplus can be interpreted as the wealth of a venture capital, whose profits depend on research and development. In most of the existing literature of dual risk models, the profits follow the compound Poisson model and the cost is constant. In this paper, we develop a state-dependent dual risk model, in which the arrival rate of the profits and the costs depend on the current state of the wealth process. Ruin probabilities are obtained in closed-forms. Further properties and results will also be discussed.

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  • Lingjiong Zhu, 2015. "A State-Dependent Dual Risk Model," Papers 1510.03920, arXiv.org.
  • Handle: RePEc:arx:papers:1510.03920
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    File URL: http://arxiv.org/pdf/1510.03920
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    References listed on IDEAS

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    1. Zhu, Lingjiong, 2013. "Moderate deviations for Hawkes processes," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 885-890.
    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. Dassios, Angelos & Zhao, Hongbiao, 2012. "Ruin by dynamic contagion claims," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 93-106.
    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.
    5. Ng, Andrew C.Y., 2010. "On the Upcrossing and Downcrossing Probabilities of a Dual Risk Model With Phase-Type Gains," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 40(01), pages 281-306, May.
    6. 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.
    7. Zhu, Lingjiong, 2013. "Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 544-550.
    8. Yang, Chen & Sendova, Kristina P., 2014. "The ruin time under the Sparre-Andersen dual model," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 28-40.
    9. Cheung, Eric C.K. & Drekic, Steve, 2008. "Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 399-422, November.
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    Cited by:

    1. Arash Fahim & Lingjiong Zhu, 2016. "Asymptotic Analysis for Optimal Dividends in a Dual Risk Model," Papers 1601.03435, arXiv.org, revised Feb 2016.
    2. Arash Fahim & Lingjiong Zhu, 2015. "Optimal Investment in a Dual Risk Model," Papers 1510.04924, arXiv.org.

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