# Edikan E. Akpanibah and Bright O. Osu, Portfolio Strategy for an Investor with Stochastic Premium Under Exponential Utility via Legendre Transform and Dual Theory, Volume 2017, Number 6, Pages 27-35, 2017

**Abstract:** We investigate the optimal investment strategies of an insurance company. We assume that the rates at which premiums are paid to insurance companies are stochastic, the total claims are modeled by a compound Poisson process, we assume that surplus of the insurance company is invested in risk free asset and in a risky asset such as stocks. We applied the Jacobi Hamilton-Jacobi-Bellman equation to obtain an optimized problem and used the Legendre transform and dual theory to obtain the optimal investment strategy for constant absolute risk aversion (CARA) utility function. Our result will enables insurance companies to determine the proportion of their wealth to be invested in risk-free asset and a risky asset in order to optimize profit knowing full well it has responsibility to pay the policy holders whenever there is claims occurrence.

**Key words:** Investment Strategy, Stochastic Premium ,Under Exponential Utility, Legendre Transform and Dual Theory.

**How to cite this article:**

Edikan E. Akpanibah and Bright O. Osu, Portfolio Strategy for an Investor with Stochastic Premium Under Exponential Utility via Legendre Transform and Dual Theory, International Journal of Advances in Mathematics, Volume 2017, Number 6, Pages 27-35, 2017.