# Weak Limits of Random Coefficient Autoregressive Processes and their Application in Ruin Theory

## TL;DR

This paper demonstrates that certain discrete-time insurance surplus processes converge to a generalized Ornstein-Uhlenbeck process, enabling approximations for ruin-related metrics crucial in risk management.

## Contribution

It establishes weak convergence of a broad class of processes to a generalized Ornstein-Uhlenbeck process and applies this to approximate ruin probabilities and related measures.

## Key findings

- Convergence of surplus processes to Ornstein-Uhlenbeck process
- Approximate ruin probabilities using the limiting process
- Enhanced methods for ruin-related risk assessments

## Abstract

We prove that a large class of discrete-time insurance surplus processes converge weakly to a generalized Ornstein-Uhlenbeck process, under a suitable re-normalization and when the time-step goes to 0. Motivated by ruin theory, we use this result to obtain approximations for the moments, the ultimate ruin probability and the discounted penalty function of the discrete-time process.