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On the total operating costs up to default in a renewal risk model

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  • Feng, Runhuan

Abstract

The paper proposes a new approach to study a general class of ruin-related quantities in the context of a renewal risk model. While the classical approaches in Sparre Andersen models have their own merits, the approach presented in this paper has its advantages from the following perspectives. (1) The underlying surplus process has the flexibility to reflect a broad range of scenarios for surplus growth including dividend policies and interest returns. (2) The solution method provides a general framework to unify a great variety of existing ruin-related quantities such as Gerber-Shiu functions and the expected present value of dividends paid up to ruin, and facilitates derivations of new ruin-related quantities such as the expected present value of total claim costs up to ruin, etc. In the end, many specific examples are explored to demonstrate its application in renewal risk models.

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  • Feng, Runhuan, 2009. "On the total operating costs up to default in a renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 305-314, October.
    • Handle: RePEc:eee:insuma:v:45:y:2009:i:2:p:305-314
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    References listed on IDEAS

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    1. 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.
    2. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    3. Albrecher, Hansjorg & Claramunt, M.Merce & Marmol, Maite, 2005. "On the distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 324-334, October.
    4. Hans Gerber & Elias Shiu, 2005. "The Time Value of Ruin in a Sparre Andersen Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 49-69.
    5. Lin, X.Sheldon & Pavlova, Kristina P., 2006. "The compound Poisson risk model with a threshold dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 57-80, February.
    6. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    7. Li, Shuanming & Garrido, Jose, 2004. "On a class of renewal risk models with a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 691-701, December.
    8. Dickson, David C. M. & Drekic, Steve, 2004. "The joint distribution of the surplus prior to ruin and the deficit at ruin in some Sparre Andersen models," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 97-107, February.
    9. Jacobsen, Martin, 2003. "Martingales and the distribution of the time to ruin," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 29-51, September.
    10. Li, Shuanming & Garrido, Jose, 2004. "On ruin for the Erlang(n) risk process," Insurance: Mathematics and Economics, Elsevier, vol. 34(3), pages 391-408, June.
    11. Hanspeter Schmidli, 2005. "“The Time Value of Ruin in a Sparre Andersen Model,” Hans U. Gerber and Elias S. W. Shiu, July 2005," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 69-70.
    12. Bangwon Ko, 2007. "“The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model”, Jiandong Ren, July 2007," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 136-137.
    13. Willmot, Gordon E., 2004. "A note on a class of delayed renewal risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 251-257, April.
    14. Albrecher, Hansjorg & Boxma, Onno J., 2005. "On the discounted penalty function in a Markov-dependent risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 650-672, December.
    15. 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.
    16. Jiandong Ren, 2007. "The Discounted Joint Distribution of the Surplus Prior to Ruin and the Deficit at Ruin in a Sparre Andersen Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 128-136.
    17. Sheldon Lin, X. & E. Willmot, Gordon & Drekic, Steve, 2003. "The classical risk model with a constant dividend barrier: analysis of the Gerber-Shiu discounted penalty function," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 551-566, December.
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    Cited by:

    1. Cheung, Eric C.K. & Feng, Runhuan, 2013. "A unified analysis of claim costs up to ruin in a Markovian arrival risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 98-109.
    2. Teng, Ye & Zhang, Zhimin, 2023. "Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    3. Cheung, Eric C.K., 2013. "Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 343-354.
    4. Cheung, Eric C.K. & Liu, Haibo & Willmot, Gordon E., 2018. "Joint moments of the total discounted gains and losses in the renewal risk model with two-sided jumps," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 358-377.
    5. Cheung, Eric C.K., 2011. "A generalized penalty function in Sparre Andersen risk models with surplus-dependent premium," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 384-397, May.
    6. Feng, Runhuan, 2011. "An operator-based approach to the analysis of ruin-related quantities in jump diffusion risk models," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 304-313, March.
    7. Feng, Runhuan & Shimizu, Yasutaka, 2014. "Potential measures for spectrally negative Markov additive processes with applications in ruin theory," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 11-26.
    8. Eric C.K. Cheung & Haibo Liu & Jae-Kyung Woo, 2015. "On the Joint Analysis of the Total Discounted Payments to Policyholders and Shareholders: Dividend Barrier Strategy," Risks, MDPI, vol. 3(4), pages 1-24, November.
    9. Wong, Jeff T.Y. & Cheung, Eric C.K., 2015. "On the time value of Parisian ruin in (dual) renewal risk processes with exponential jumps," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 280-290.

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