Research on ruin probability of risk model based on AR(1) series

TL;DR

This paper develops a risk model based on AR(1) series with dependent claim structures, using Newton iteration to estimate ruin probabilities, thereby advancing ruin theory and supporting stable insurance industry growth.

Contribution

Introduces a novel AR(1)-based risk model with dependent claim structure and applies Newton iteration to estimate ruin probabilities, enhancing theoretical understanding.

Findings

Derived exponential upper bounds for ruin probability.

Estimated the adjustment coefficient using Newton iteration.

Provided a new approach to ruin probability estimation in dependent models.

Abstract

In this text, we establish the risk model based on AR(1) series and propose the basic model which has a dependent structure under intensity of claim number. Considering some properties of the risk model, we take advantage of newton iteration method to figure out the adjustment coefficient and estimate the exponential upper bound of ruin probability. This is significant to refine the research of ruin theory. As a result, our theory will help develop insurance industry stably.