كران براي توزيع توام سرمايه قبل و در هنگام ورشكستگي

5. Bound for the Joint Distribution of the Surplus, Prior to and at Ruin

In this article, we study the (bivariate) tail of the joint distribution of the surplus prior to and at ruin, for the classical risk model with Poisson arrivals, and, some exact expressions and new bounds for this tail are achieved. Three numerical methods that may yield upper are lower bounds for it are offered by Politics and Psarrakos (2008), and the author suggests a new numerical lower bound. Also, new upper and lower bounds for the probability of ruin are provided as a by-product of analysis, many of the bounds provided in the current paper improve and generalize corresponding bounds that have been appeared earlier. At the end, the performance of the new lower bound which is introduced in this paper is compared with current methods in case of a numerical example with real data (the data is associated with the freight insurance on the license of the Iran Insurance Company and the results are considerable).