Paper Title
Optimal Proportion Decision-Making Of Two-Stage Investment With Jump Risk

Abstract
This paper examines time and amount to invest in a project with uncertain expected future cash flow. Two-stage investment decision supplies managerial flexibilities to project managers whose responsibility is to decide when and how much proportion of the total budget they should invest, as the total fund of a certain project would be approved by top executives or board of directors. This paper found that the value of a project is higher by split the installment into two stages rather than invest all at once. The waiting time of the first investment of the two-stage is shorter than that of one-stage, but that of the second investment is longer. The volatility increases waiting time and optimal investment proportion of two-stage. The model in this paper also includes a onetime event that cause the value of the project to be vanish. Such jump downside risk pressures the company to wait longer to invest in one-stage, first stage and second stage. Under medium and high volatility, the higher the mean arrival rate of event, the higher the optimal proportion. Nevertheless, the lower optimal proportion is associate with higher mean arrival rate when the volatility is low. Keywords - Real option, Sequential investment, Investment proportion, Uncertainty, Jump risk