IJAM, Volume 26, No. 5 (2013)

Abstract. This paper study the optimal net investment wealth with discounted stochastic cash flows for a certain investor who trades in complete diffusion models, receives a stochastic cash inflows and pays a stochastic cash outflows. The cash inflows and cash outflows are correlated to the index bond and stock market risks over time. This paper aims at determining the optimal variational Merton portfolio, expected final net investment wealth and its variance and efficient frontier for the three classes of assets: stock, index bond and cash account. The discounted cash inflows and outflows are obtained. The dynamics of the net investment wealth process involving two risky assets and a cash account is obtained. We further established the market efficiency test and efficient frontier for the final net investment wealth process of the investor. We obtain the optimal terminal net investment wealth and show that the discounted cash inflows and cash outflows depend on the optimal wealth of the investor. The expected terminal net investment wealth with zero variance is established. Some numerical results were illustrated in this paper.