Optimizing the returns and Probability of Survival of Insurance Company with time varying Investment returns

Abstract

This study focuses on obtaining investment strategies that are optimal in the sense of optimizing the returns and the probability of survival of an insurance company. we take the risk reserve of an insurance company to follow Brownian motion with drift and tackle an optimal portfolio selection problem of the company. The investment case considered was insurance company that trades two assets: the money market account (bond) growing at a rate that is linear function of time anda risky stock with an investment behavior in the presence of a stochastic cash flow or a risk process, continuously in the economy. In particular we solved for the strategy that optimizes the probability of achieving a given upper wealth level before hitting a given lower level. We established among others that, the optimized investment in the risky asset (stock) is horizon dependent and the wealth and the optimal value function of the probability of survival for both utility functions are same.