一类离散相依索赔风险模型的随机分红问题

Abstract

Abstract:

In this paper, the compound binomial risk model is extended by involving the random premium income with time-correlated claims and random dividend strategy. By the method of generating function, the difference equation and its solution for the expected cumulated discounted dividends until ruin are obtained. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples.

Key words: The expected cumulated discounted dividends, Time-correlated claims, Stochastic premium income, Randomized dividend policy

CLC Number:

O211.6

Mi Chen,Changwei Nie,Haiyan Liu. Randomized Dividends in a Discrete Risk Model with Time-Correlated Claims[J].Acta mathematica scientia,Series A, 2022, 42(2): 631-640.

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Figures/Tables 3

References 26

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$V(u, b)$	$u=0$	$u=1$	$u=2$	$u=3$	$u=4$	$u=5$	$u=6$	$u=7$	$u=8$
$v=0.96$	1.3615	1.6118	1.8653	2.0968	2.1991	2.2684	2.3146	2.3449	2.3649
$v=0.93$	0.6677	0.8219	0.9908	1.1639	1.2221	1.2614	1.2873	1.3041	1.3150
$v=0.90$	0.3999	0.5123	0.6439	0.7910	0.8309	0.8579	0.8579	0.8873	0.8950

$V(u, b)$	$u=0$	$u=1$	$u=2$	$u=3$	$u=4$	$u=5$	$u=6$	$u=7$	$u=8$
$\theta=0$	0.7612	0.9249	1.0882	1.2519	1.4327	1.6373	1.8703	2.1362	2.4399
$\theta=0.25$	0.7121	0.8950	1.0591	1.2205	1.3975	1.5972	1.8246	2.0840	2.3803
$\theta=0.5$	0.6689	0.8687	1.0336	1.1930	1.3665	1.5620	1.7845	2.0382	2.3279
$\theta=0.75$	0.6307	0.8454	1.0109	1.1686	1.3391	1.5309	1.7489	1.9976	2.2816
$\theta=1$	0.5966	0.8246	0.9908	1.1468	1.3147	1.5031	1.7172	1.9614	2.2403

$V(u, b)$	$b=1$	$b=2$	$b=3$	$b=4$	$b=5$	$b=6$	$b=7$	$b=8$	$b=9$	$b=10$
$u=1$	1.6893	1.4971	1.3001	1.1123	0.9449	0.8003	0.6765	0.5710	0.4816	0.4058
$u=2$	1.9841	1.9125	1.6609	1.4209	1.2072	1.0223	0.8642	0.7296	0.6153	0.5184
$u=3$	2.2042	2.1461	2.0305	1.7371	1.4759	1.2499	1.0565	0.8919	0.7522	0.6338
$u=4$	2.3646	2.3201	2.2204	2.0786	1.7660	1.4955	1.2641	1.0672	0.9001	0.7584
$u=5$	2.4837	2.4489	2.3625	2.2405	2.0902	1.7701	1.4963	1.2632	1.0654	0.8976

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Randomized Dividends in a Discrete Risk Model with Time-Correlated Claims

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