Ruin Probabilities And Local Ruin Probabilities In The Multi-delayed Renewal Risk Model

Ruin probability is traditionally considered as part of insurance mathematics, and has been an active area of research from 1930's all the way up to today. A flood of papers have been published on this topic since then. For example, research on ruin probabilities in the classical renewal risk model has already been mature (see [1] et al.). In recent years, ruin probabilities in the delayed renewal risk model have been studied (see [2] et al.). However, the above research has been mainly concentrated on the renewal risk model with heavy-tailed (large) claims, moroever, sometimes only a delayed inter-arrival time can not reflect the complex actual situation. The first motive of the present paper is to extend the number of delayed inter-arrival time(s) from 1 to arbitrarily finite, and to investigate asymptotic behavior for ruin probabilities in the multi-delayed renewal risk model with light-tails. Chapter 2 delivers asymptotic forms for ruin probabilities in the multi-delayed renewal risk model with large claims as well as light tails. Recently, particular interest has been contributed to local ruin probabilities in the renewal risk model (see [3], [4] et al.), but the related renewal risk model usually is ordinary or only one-delayed. So the second motive of the present paper is to investigate asymptotic behavior for local ruin probabilities with the renewal risk model extended from ordinary or one-delayed to multi-delayed, we establish asymptotic estimates for local ruin probabilities in the multi-delayed renewal risk model with large claims as well as small claims. As a special case, we deliver a concrete asymptotic formula for local ruin probability in the multi-delayed Erlang (n, A) risk model. These contents will appear in Chapter 3.