Ruin models with investment income

TL;DR

This survey reviews ruin probability models incorporating investment income, discussing equations, solutions, bounds, and control strategies mainly in continuous time, with extensive references for further research.

Contribution

It provides a comprehensive overview of ruin models with investment income, including recent developments, solution methods, and control strategies, especially in continuous time frameworks.

Findings

Presentation of integro-differential equations for ruin probability

Analysis of exact and numerical solutions

Discussion of bounds and control strategies

Abstract

This survey treats the problem of ruin in a risk model when assets earn investment income. In addition to a general presentation of the problem, topics covered are a presentation of the relevant integro-differential equations, exact and numerical solutions, asymptotic results, bounds on the ruin probability and also the possibility of minimizing the ruin probability by investment and possibly reinsurance control. The main emphasis is on continuous time models, but discrete time models are also covered. A fairly extensive list of references is provided, particularly of papers published after 1998. For more references to papers published before that, the reader can consult [47].