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On the Compound Beta-Binomial Risk Model with Delayed Claims and Randomized Dividends

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  • Aparna B. S
  • Neelesh S Upadhye

Abstract

In this paper, we propose the discrete time Compound Beta-Binomial Risk Model with by-claims, delayed by-claims and randomized dividends. We then analyze the Gerber-Shiu function for the cases where the dividend threshold $d=0$ and $d>0$ under the assumption that the constant discount rate $\nu \in (0,1)$. More specifically, we study the discrete time compound binomial risk model subject to the assumption that the probabilities with which the claims, by-claims occur and the dividends are issued are not fixed(constant), instead the probabilities are random and follow a Beta distribution with parameters $a_{i}$ and $b_{i}$, $i = 1, 2, 3$. Recursive expressions for the Gerber-Shiu function corresponding to the proposed model are obtained. The recursive relations are further utilized to obtain significant ruin related quantities of interest. Recursive relations for probability of ruin, the probability of the deficit at ruin, the generating function of the deficit at ruin and the probability of surplus at ruin and for the probability of the claim causing ruin are obtained.

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  • Aparna B. S & Neelesh S Upadhye, 2019. "On the Compound Beta-Binomial Risk Model with Delayed Claims and Randomized Dividends," Papers 1908.03407, arXiv.org.
    • Handle: RePEc:arx:papers:1908.03407
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    References listed on IDEAS

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    8. Kam Pui Wat & Kam Chuen Yuen & Wai Keung Li & Xueyuan Wu, 2018. "On the Compound Binomial Risk Model with Delayed Claims and Randomized Dividends," Risks, MDPI, vol. 6(1), pages 1-13, January.
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    Cited by:

    1. Yue He & Reiichiro Kawai & Yasutaka Shimizu & Kazutoshi Yamazaki, 2022. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Papers 2203.10680, arXiv.org, revised Dec 2022.

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