Optimal Control of Investment for an Insurer in Two Currency Markets

TL;DR

This paper develops a model for an insurer's optimal investment strategy across two currency markets, incorporating foreign exchange rate dynamics and using dynamic programming to derive solutions.

Contribution

It introduces a novel framework for optimal investment in dual currency markets with stochastic exchange rates modeled by Ornstein-Uhlenbeck processes.

Findings

Derived explicit optimal investment strategies.

Provided numerical analysis illustrating strategy effectiveness.

Extended classical models to include foreign exchange risk.

Abstract

In this paper, we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model. Investment in the foreign market is allowed, and therefore, the foreign exchange rate model is considered and incorporated. It is assumed that the instantaneous mean growth rate of foreign exchange rate price follows an Ornstein-Uhlenbeck process. Dynamic programming method is employed to study the problem of maximizing the expected exponential utility of terminal wealth. By soloving the correspoding Hamilton-Jacobi-Bellman equations, the optimal investment strategies and the value functions are obtained. Finally, numerical analysis is presented.