# Optimal Reinsurance and Investment in a Diffusion Model

## TL;DR

This paper develops a model for optimal reinsurance and investment strategies in a stochastic environment, providing explicit solutions for specific reinsurance types under a diffusion approximation.

## Contribution

It introduces a diffusion-based framework incorporating environmental factors for reinsurance and investment optimization, with explicit solutions for proportional and excess-of-loss reinsurance.

## Key findings

- Explicit solutions for proportional reinsurance
- Explicit solutions for excess-of-loss reinsurance
- Maximization of terminal expected utility in a stochastic environment

## Abstract

We consider a diffusion approximation to an insurance risk model where an external driver models a stochastic environment. The insurer can buy reinsurance. Moreover, investment in a financial market is possible. The financial market is also driven by the environmental process. Our goal is to maximise terminal expected utility. In particular, we consider the case of SAHARA utility functions. In the case of proportional and excess-of-loss reinsurance, we obtain explicit results.