Baltrūnas, Aleksandras; Leipus, Remigijus; Šiaulys, Jonas Precise large deviation results for the total claim amount under subexponential claim sizes. (English) Zbl 1145.60018 Stat. Probab. Lett. 78, No. 10, 1206-1214 (2008). Summary: The paper deals with the renewal risk model. A precise large deviation result in the case of subexponential claim sizes is proved. As a special case, the example of Pareto distributed claim sizes and inter-occurrence times is investigated. Cited in 23 Documents MSC: 60F10 Large deviations 91B30 Risk theory, insurance (MSC2010) Keywords:renewal risk model; subexponential claim sizes PDFBibTeX XMLCite \textit{A. Baltrūnas} et al., Stat. Probab. Lett. 78, No. 10, 1206--1214 (2008; Zbl 1145.60018) Full Text: DOI HAL References: [1] Baltrūnas, A.; Daley, D. J.; Klüppelberg, C., Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times, Stochastic Process. Appl., 111, 237-258 (2004) · Zbl 1082.60080 [2] Baltrūnas, A., Second order behaviour of ruin probabilities in the case of large claims, Insurance Math. Econom., 36, 485-498 (2005) · Zbl 1120.62091 [3] Embrechts, P.; Klüppelberg, C.; Mikosch, T., Modeling Extremal Events (1997), Springer: Springer Berlin [4] Klüppelberg, C.; Mikosch, T., Large deviations of heavy-tailed random sums with applications in insurance and finance, J. Appl. Probab., 34, 293-308 (1997) · Zbl 0903.60021 [5] Mikosch, T.; Nagaev, A. V., Large deviations of heavy-tailed sums with applications in insurance, Extremes, 1, 81-110 (1998) · Zbl 0927.60037 [6] Ng, K. W.; Tang, Q.; Yan, J.; Yang, H., Precise large deviations for sums of random variables with consistently varying tails, J. Appl. Probab., 41, 93-107 (2004) · Zbl 1051.60032 [7] Tang, Q.; Su, C.; Jiang, T.; Zhang, J., Large deviations for heavy-tailed random sums in compound renewal model, Statist. Probab. Lett., 52, 91-100 (2001) · Zbl 0977.60034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.