# Optimal excess-of-loss reinsurance and investment problem for an insurer with default risk under a stochastic volatility model

## TL;DR

This paper derives optimal reinsurance and investment strategies for an insurer in a defaultable market with stochastic volatility, maximizing utility and providing explicit solutions and numerical insights.

## Contribution

It introduces a comprehensive model for optimal reinsurance and investment under default risk and stochastic volatility, with explicit solutions and numerical analysis.

## Key findings

- Explicit optimal strategies derived for pre-default and post-default cases.
- Existence and uniqueness of solutions established via verification theorem.
- Numerical results in the Scott model provide economic insights.

## Abstract

In this paper, we study an optimal excess-of-loss reinsurance and investment problem for an insurer in defaultable market. The insurer can buy reinsurance and invest in the following securities: a bank account, a risky asset with stochastic volatility and a defaultable corporate bond. We discuss the optimal investment strategy into two subproblems: a pre-default case and a post-default case. We show the existence of a classical solution to a pre-default case via super-sub solution techniques and give an explicit characterization of the optimal reinsurance and investment policies that maximize the expected CARA utility of the terminal wealth. We prove a verification theorem establishing the uniqueness of the solution. Numerical results are presented in the case of the Scott model and we discuss economic insights obtained from these results.