Volume 29, Issue 3
On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

Commun. Math. Res., 29 (2013), pp. 193-202.

Published online: 2021-05

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• Abstract

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for $K_n$ claim amount distributions. Numerical illustrations are also given.

• AMS Subject Headings

62P05, 91B30

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@Article{CMR-29-193, author = {Xie , Jiehua and Zou , Wei}, title = {On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {3}, pages = {193--202}, abstract = {

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for $K_n$ claim amount distributions. Numerical illustrations are also given.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19003.html} }
TY - JOUR T1 - On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims AU - Xie , Jiehua AU - Zou , Wei JO - Communications in Mathematical Research VL - 3 SP - 193 EP - 202 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19003.html KW - compound binomial model, delayed claim, dividend, expected present value. AB -

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for $K_n$ claim amount distributions. Numerical illustrations are also given.

Jiehua Xie & Wei Zou. (2021). On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims. Communications in Mathematical Research . 29 (3). 193-202. doi:
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