Fang, Shizu; Zhao, Peichen; Zhang, Chunmei The expected discounted penalty function at ruin of the discrete risk model with random income. (English) Zbl 1174.91486 Math. Appl. 21, No. 4, 771-777 (2008). 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. Cited in 1 Document MSC: 91B30 Risk theory, insurance (MSC2010) 62P05 Applications of statistics to actuarial sciences and financial mathematics Keywords:discounted penalty function; compound binomial process; recursive formula; discrete renewal equation; asymptotic estimate PDFBibTeX XMLCite \textit{S. Fang} et al., Math. Appl. 21, No. 4, 771--777 (2008; Zbl 1174.91486)