This study considers 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 r_t= ε+σt 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. Also transaction cost reduced the optimal investment in the risky asset by a fraction of the insurer’s wealth, It is recommended that the managers of the assets of the insurance company should take into consideration this horizon dependency when making policy decisions.
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