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The expected discounted penalty function at ruin of the discrete risk model with random income. (English) Zbl 1174.91486

Summary: In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. We examine the expected discounted value of a penalty at ruin, which is considered as a function of the initial surplus. A mathematically recursive formula is derived for the expected discounted penalty function, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give some examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty functions.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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