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Optimal Dividends Under a Ruin Probability Constraint

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  • Dickson, D. C. M.
  • Drekic, S.

Abstract

We consider a classical surplus process modified by the payment of dividends when the insurer's surplus exceeds a threshold. We use a probabilistic argument to obtain general expressions for the expected present value of dividend payments, and show how these expressions can be applied for certain individual claim amount distributions. We then consider the question of maximising the expected present value of dividend payments subject to a constraint on the insurer's ruin probability.

Suggested Citation

  • Dickson, D. C. M. & Drekic, S., 2006. "Optimal Dividends Under a Ruin Probability Constraint," Annals of Actuarial Science, Cambridge University Press, vol. 1(2), pages 291-306, September.
    • Handle: RePEc:cup:anacsi:v:1:y:2006:i:02:p:291-306_00
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    Cited by:

    1. Liu, Zaiming & Li, Manman & Ameer, Sherbaz, 2009. "Methods for estimating optimal Dickson and Waters modification dividend barrier," Economic Modelling, Elsevier, vol. 26(5), pages 886-892, September.
    2. Manman, Li & Zaiming, Liu & Hua, Dong, 2011. "Estimates for the optimal control policy in the presence of regulations and heavy tails," Economic Modelling, Elsevier, vol. 28(1), pages 482-488.
    3. Yiqing Chen & Jiajun Liu & Yang Yang, 2023. "Ruin under Light-Tailed or Moderately Heavy-Tailed Insurance Risks Interplayed with Financial Risks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    4. Soren Christensen & Kristoffer Lindensjo, 2019. "Moment constrained optimal dividends: precommitment \& consistent planning," Papers 1909.10749, arXiv.org.
    5. Zhu, Jinxia & Chen, Feng, 2015. "Dividend optimization under reserve constraints for the Cramér–Lundberg model compounded by force of interest," Economic Modelling, Elsevier, vol. 46(C), pages 142-156.
    6. Manman, Li & Zaiming, Liu & Hua, Dong, 2011. "Estimates for the optimal control policy in the presence of regulations and heavy tails," Economic Modelling, Elsevier, vol. 28(1-2), pages 482-488, January.
    7. Ramsden, Lewis & Papaioannou, Apostolos D., 2019. "On the time to ruin for a dependent delayed capital injection risk model," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 119-135.
    8. Gerber, Hans U. & Shiu, Elias S.W. & Smith, Nathaniel, 2008. "Methods for estimating the optimal dividend barrier and the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 243-254, February.

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