Approximations and upper bounds on probabilities of large deviations in the problem of ruin within finite time

Abstract

In the framework of Andersen's risk model, a new asymptotic expression and upper bounds on probabilities of ruin after time t(u) ≫ and before time 0 < t(u) ≪ , as the initial risk reserve u increases to infinity, are suggested. This result complements the classical normal-type approximation for the probability of ruin within finite time and is designed as its large deviations counterpart. The main technical device of the paper (see Section 3), which is of independent interest, are the upper bounds and the asymptotic expressions for the probabilities of large deviations of the stopped random walks, developed under low moment conditions.

Key words:

• Anderson model
• finite time ruin probability
• large deviations
• low moment conditions

Additional information

Notes on contributors

Vsevolod Malinovskii

The research described in this publication was supported in part by Grant No. JB7100 from the International Science Foundation and Russian Government.