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Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends

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  • Sung Soo Kim

    (Department of Statistics & Actuarial Science, University ofWaterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada)

  • Steve Drekic

    (Department of Statistics & Actuarial Science, University ofWaterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada)

Abstract

We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin associated with this model. We investigate several numerical examples and make some observations concerning the impact our threshold levels have on the finite-time ruin probabilities and expected total discounted dividends paid prior to ruin.

Suggested Citation

  • Sung Soo Kim & Steve Drekic, 2016. "Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends," Risks, MDPI, vol. 4(1), pages 1-15, February.
    • Handle: RePEc:gam:jrisks:v:4:y:2016:i:1:p:2-:d:63362
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    References listed on IDEAS

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    1. Cai, Jun & Dickson, David C.M., 2004. "Ruin probabilities with a Markov chain interest model," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 513-525, December.
    2. Dickson, David C.M. & dos Reis, Alfredo D. Egídio & Waters, Howard R., 1995. "Some Stable Algorithms in Ruin Theory and Their Applications," ASTIN Bulletin, Cambridge University Press, vol. 25(2), pages 153-175, November.
    3. Alfa, Attahiru Sule & Drekic, Steve, 2007. "Algorithmic Analysis of the Sparre Andersen Model in Discrete Time," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 293-317, November.
    4. Steve Drekic & Ana Maria Mera, 2011. "Ruin Analysis of a Threshold Strategy in a Discrete-Time Sparre Andersen Model," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 723-747, December.
    5. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    6. Korn, Ralf & Wiese, Anke, 2008. "Optimal Investment and Bounded Ruin Probability: Constant Portfolio Strategies and Mean-variance Analysis 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 423-440, November.
    7. Dickson, David C.M. & Waters, Howard R., 2004. "Some Optimal Dividends Problems," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 49-74, May.
    8. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    9. Cossette, Helene & Landriault, David & Marceau, Etienne, 2006. "Ruin probabilities in the discrete time renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 309-323, April.
    10. Cheung, Eric C.K. & Landriault, David & Willmot, Gordon E. & Woo, Jae-Kyung, 2010. "Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 117-126, February.
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    Cited by:

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