Abstract
The compound binomial insurance risk model is extended to the case where the premium income process, based on a binomial process, is no longer a constant premium rate of 1 per period and insurer pays a dividend of 1 with a probabilityq0when the surplus is greater than or equal to a nonnegative integerb. The recursion formulas for expected discounted penalty function are derived. As applications, we present the recursion formulas for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin. Finally, numerical example is also given to illustrate the effect of the related parameters on the ruin probability.
Highlights
The classical compound binomial insurance risk model is a discrete time risk process with the following features
We assume that claims occur at the end of the period and denote by ξt = 1 the event where a claim occurs in the time period
We consider a discrete time risk process based on the compound binomial model, which is the extension of the work of Tan and Yang [11]
Summary
The classical compound binomial insurance risk model is a discrete time risk process with the following features. For the compound binomial model, Tan and Yang [11] consider the risk model (1) modified by the inclusion of dividends and derive recursion formulas and an asymptotic estimate for the ruin probability, the probability function of the surplus prior to the ruin time, and the severity of ruin, and so forth. We suppose that the insurer will pay a dividend of 1 with a probability q0 (0 ≤ q0 < 1) in each time period if the surplus is greater than or equal to a nonnegative integer b at the beginning of the period It implies that the randomized dividend payments will only possibly occur at the beginning of each period, right after receiving the stochastic premium payment. A numerical example is given to illustrate the effect of parameters on the ruin probability
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