# Ruin probabilities in the Cram\'er-Lundberg model with temporarily negative capital

## TL;DR

This paper investigates the asymptotic behavior of ruin probabilities in a modified Cramér-Lundberg model where negative capital does not immediately imply ruin, analyzing how this affects classical ruin probability estimates under various conditions.

## Contribution

It introduces a generalized ruin concept allowing for survival mechanisms during negative capital periods and studies its asymptotic relation to classical ruin probabilities.

## Key findings

- Asymptotics of modified ruin probability are characterized under Cramér and subexponential conditions.
- The modified model's ruin probability behaves similarly to classical models under broad assumptions.
- Results extend classical ruin theory to models with temporary negative capital.

## Abstract

We study the asymptotics of the ruin probability in the Cram\'er-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive due to certain mechanisms. Under a rather general assumption on the mechanism - satisfied by most such modified models from the literature - we study the relation of the asymptotics of the modified ruin probability to the classical ruin probability. This is done under the Cram\'er condition as well as for subexponential integrated claim sizes.