On the probability and the time of insurance ruin. (English) Zbl 1143.60024

Summary: The estimation of ruin probability has been the central topic in insurance risk theory. In this paper we study the asymptotic behavior of the probability of ruin and the probability that ruin occurs before the end of planning years in the compound Poisson model. The exponential bounds for both probabilities are found to be functions of the rate function in traditional large deviation theory.


60F10 Large deviations
60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
91B30 Risk theory, insurance (MSC2010)