Abstract
This paper extends the work of Yuen et al. (2013), who obtained explicit results for the discount-free Gerber–Shiu function for a compound binomial risk model in the presence of delayed claims and a randomized dividend strategy with a zero threshold level. Specifically, we establish a recursion method for computing the Gerber–Shiu expected discounted penalty function, which entails a number of important quantities in ruin theory, within the framework of the compound binomial aggregate claims with delayed by-claims and randomized dividends payable at a non-negative threshold level.
Highlights
The compound binomial risk model is a class of discrete-time and discrete-valued risk processes.It was first introduced by Gerber (1988)
Li (2008) analyzed the moments of the present value of the dividends in the compound binomial model under a constant dividend barrier and stochastic interest rates. Another type of dividend paying strategy is the randomized dividend strategy, under which, when the insurance company’s surplus level is equal to or above a threshold value, dividends are payable with a certain probability
We revisit the compound binomial risk model with the above-mentioned time-correlation and randomized dividends, which has been attempted by Yuen et al (2013) in a simplified case, that is, a discount-free economic environment with a zero threshold for the randomized dividends
Summary
The compound binomial risk model is a class of discrete-time and discrete-valued risk processes. Studied expected total dividends until ruin in a discrete-time risk model with delayed claims and a constant dividend barrier. Li (2008) analyzed the moments of the present value of the dividends in the compound binomial model under a constant dividend barrier and stochastic interest rates Another type of dividend paying strategy is the randomized dividend strategy, under which, when the insurance company’s surplus level is equal to or above a threshold value, dividends are payable with a certain probability. We revisit the compound binomial risk model with the above-mentioned time-correlation and randomized dividends, which has been attempted by Yuen et al (2013) in a simplified case, that is, a discount-free economic environment with a zero threshold for the randomized dividends. The generalization enables us to better relate the risk model under consideration to real-life insurance problems such as the time value of money, and positive dividend thresholds are commonly adopted in practice
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