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Expected present value of total dividends in a delayed claims risk model under stochastic interest rates

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  • Xie, Jie-hua
  • Zou, Wei

Abstract

In this paper, a compound binomial risk model with a constant dividend barrier under stochastic interest rates is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. In the evaluation of the expected present value of dividends, the interest rates are assumed to follow a Markov chain with finite state space. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

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  • Xie, Jie-hua & Zou, Wei, 2010. "Expected present value of total dividends in a delayed claims risk model under stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 415-422, April.
    • Handle: RePEc:eee:insuma:v:46:y:2010:i:2:p:415-422
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    References listed on IDEAS

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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.
    2. Jiyang Tan & Chun Li & Ziqiang Li & Xiangqun Yang & Bicheng Zhang, 2015. "Optimal dividend strategies in a delayed claim risk model with dividends discounted by stochastic interest rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 61-83, August.
    3. Dawei Lu & Meng Yuan, 2022. "Asymptotic Finite-Time Ruin Probabilities for a Bidimensional Delay-Claim Risk Model with Subexponential Claims," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2265-2286, December.
    4. Yuan, Meng & Lu, Dawei, 2023. "Asymptotics for a time-dependent by-claim model with dependent subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 120-141.

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