Two-sided Bounds For Stop-loss Premiums In The Discrete Time Renewal Model

As is known to all, risk theory is an important branch of the modernapplied mathematics. Using the knowledge and methods in probability theory,mathematical statistics and stochastic processes, we can establish correspondingmathematical model according to the actual problems in insurance company.Ruin theory is the most important part in risk theory. In recent years, someimportant ruin quantities such as ruin probability and Stop-loss Premiums havebeen hot issues in the risk theory. However, it is difficult to get explicitexpressions for those ruin quantities; an effective method is to give theircorresponding estimation of the upper and lower bounds.In this paper we mainly study the estimation of the upper and lowerbounds for Stop-loss premiums in the ordinary discrete time renewal model. In the second chapter, we give the definition and expression of Stop-loss premiumsπ_S(x)in the ordinary discrete time renewal model. More precisely, in thesecond section we obtain five two sided bounds for π_S(x). We givecorresponding numerical results by using the theory of two-sided bounds forpremiums in the third section.In the third chapter, we aim to give new upperbounds for π_S(x)when the ladder distribution is decreasing. In the first sectionwe give five upper bounds for π_S(x). When the claim amounts followgeometrical distribution and shifted negative binomial distribution, numericalexamples are presented in the second section. The results obtained in this papersupplement the related study of stop-loss premiums.