Optimization of insurance broker's investment, consumption and the probability of survival with constant rate of return under exponential utility function

Abstract

In this study, we take the risk reserve of an insurance broker to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance broker that trades two assets: the money market account (bond) growing at a rate  and a risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy. Our focus was on obtaining investment strategies that are optimal in the sense of optimizing the returns of the company. We established among others that, the optimized investment in the assets and the optimal value function are dependent on horizon and the wealth. It is recommended that the broker should take into consideration this horizon dependency when making policy decisions.