项目投资组合选择是许多风险投资公司的重要决策问题，风险投资公司利用有限的资源通过选择和执行项目组合试图创造价值，而风险投资家的行为偏好直接影响最优项目组合选择的结果。通常，风险项目的价值是不确定的，因此风险投资家必须基于对风险项目未来价值的事前估计进行投资决策。在展望理论框架下，构建了考虑风险投资家损失厌恶心理特征的风险项目投资组合优化模型，给出了处理项目组合选择中价值估计不确定性的贝叶斯方法，并应用Monte Carlo模拟将模型转化为线性整数规划问题。研究发现，相对于直接基于事前价值估计的投资组合选择，对项目价值事前估计不确定性的贝叶斯建模可以给出更加精确的价值估计，并使用所获得的修正估计进行投资组合决策，可以帮助选择具有更高的事后期望效用的项目组合，消除估计的事前期望效用与事后实现的期望效用之间的预期间隔，降低风险投资家预期的决策后失望程度。
The venture capital market plays a significant role in providing capital to a new feasible business idea(new product, service, or retail concept) and businesses of different type. Project portfolio selection is an important decision in many venture capital companies, and practically all venture capitalists(VC) seek to creat value by selecting and executing portfolios of venture projects that consume resourse, and behavioral factors of the VC directly influences the result of the optimal portfolio selection. Most studies on project portfolio selection focus on identifying the "right" project portfolio under various criteria, such as reward and risk.
In this paper a portfolio approach is taken to analyze the investment strategy of aVC. Considering the psych-ological characteristics of VC's loss aversion from the perspective of prospect theory, a more practical portfolio optimization model that maximizes the expected utility of VC is constructed, and the model is transformed into a linear mixed integer programming problem by the Monte Carlo simulation method.
Typically, the value of venture capital project is uncertain,and thus venture capitalist must take decisions based on ex ante estimates about what this future value will be. Due to estimation uncertainties, it is difficult to identify the truly best projects, whereby the selected portfolio is typically suboptimal. Furthermore, it can be shown that the value of the selected portfolio is systematically overestimated, causing the VC to experience post-decision disappointment. The phenomenon underlying post-decision disappointment is, in short, that the more the value of a project has been overestimated, the more probable it is that this project will be selected. In this paper, a Bayesian model framework to account for value uncertainties in project portfolio selection is developed. Our analytical and simulation results show that, in comparison with the straightforward portfolio selection based on ex ante value estimates, the explicit Bayesian modeling of estimation uncertainties tends to give more accurate project value estimates, resulting in a higher expected portfolio utility value, and eliminate the expected gap between the realized ex post portfolio utility value and the estimated ex ante portfolio utility value. Moreover, our results have shown that the Bayesian revision of value estimates decrease the level of disappointment that the VC can expect to experience.
With the proposed Bayesian framework VC can gather more precise information about projects' value and mitigate the experienced post-decision disappointment. Apart from the debiasing of value estimates, our frame-work could be extended by developing a model that accounts both value and cost uncertainties. This way number of targets of application could be substantially increased.
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