Search

We investigate precise large deviations for heavy-tailed random sums. We prove a general asymptotic relation in the compound renewal risk model for consistently varying-tailed distributions. This model was introduced in [Q. Tang, C. Su, T. Jiang, and J.S. Zang, Large deviation for heavy-tailed random sums in compound renewal model, Stat. Probab. Lett., 52:91-100, 2001] as a more practical risk model. The proof is based on the inequality found in [D. Fuk and S.V. Nagaev, Probability for sums of independent random variables, Theory Probab. Appl., 16:600-675, 1971]. [ABSTRACT FROM AUTHOR]

Analyzes the problem of qualitative research model by characterizing the main formulas of characterizing dynamics of the model. Development of classical results devoted to the behavior of the ruin probability under conditions of permanent inflation and constant interest force; Generalization of the Lindley chain, which was used in the risk model without interest force.