Abstract: In the process of project investment decision, investors face various risks. Some are project risks from the project itself. Some are background risks from exogenous uncertainty, such as interest rate risk, inflation risk,and so on. Based on the different effects that background risks have on the investment wealth, the background risks can be divided into additive background risks and multiplicative background risks. In practice, investors often face the two kinds of background risks as well as project risks. Besides, there often exist correlations between the background risks and project risks. The changes of the background risks will usually lead to corresponding changes of the project risks, which makes project investment decision become more complicated. Thus, it is necessary to study the problems of project investment decision considering the background risks and the correlations between the project risks and background risks.
According to the literature review, most studies on background risks focus on the impact of some kind of the background risks on the investor's risk attitude, risky asset allocation, and individual portfolio selection. The researches on project investment decision considering the background risks are limited, and those considering the additive and multiplicative background risks simultaneously are few. Therefore, a decision analysis method is proposed. In the method, project investment decision models are constructed considering the two kinds of background risks as well as project risk, and the effects of the correlations between the background risks and project risk on the investment decision are analyzed.
First of all, the project investment decision model is constructed, which considers the additive background risk and project risk and the correlations between them. In this case, the analytic solution of the optimal investment value can be obtained. When the correlation coefficient is in a certain range, there exists the optimal investment value which can maximize the certainty equivalent of the expected investment profit. Then, with respect to the situation of the multiplicative background risk, a project investment decision model is also constructed. By the simulation analysis of the model, it can be concluded that the optimal investment value exists, and the correlation coefficient between the multiplicative background risk and project risk has effect on investment decision.
Further, the investment decision model considering the two kinds of background risks is constructed. In the model, the correlation coefficients between the additive background risk and project risk and those between the multiplicative background risk and project risk are both considered. And, the monte carlo simulation is used to analyze the impacts of the correlations on investment decisions under different situations. On the basis of the analysis, the results can be obtained that there exists optimal investment value in any case. And, the influence of the correlations between the additive background risk and project risk on the investment decision is weakened. In addition, there are differences in the certainty equivalent and optimal investment value compared with the situation of the multiplicative background risk alone.
Finally, the research conclusions and limitations are summarized. Our study implies that different background risks and correlation coefficients can make the optimal investment value and investment profit different. Therefore, it is necessary to consider the two kinds of background risks and the correlations between them and the project risk in the process of the project investment decision. The research conclusions can also provide decision support for investors facing with the problem of project investment decision in practice.

Key words: background risks, additive background risk, multiplicative background risk, project investment decision