The Stochastic Optimization Model Of Project Portfolio Based On Disappointment Aversion

Actually, venture capital is that capitalists choose the portfolio based on projects' returns and risk under uncertainty, so different methods to measure the returns and risk of projects will result in different investment programs. The classical portfolio theory assumes that investors are completely rational, but in fact their investment decisions are significantly influenced by their subjective preference. Before making investment decisions, investors will analyze and evaluate the projects' values and risk, and make the final investment decisions which are fitting their objectives and preferences. So in this paper, considering the uncertainty of projects' returns and risk in future, starting from capitalists' ‘disappointment aversion' psychological, and based on the results of existing theoretical research about venture capital at home and abroad, we set up single stage and multistage stochastic optimization models of venture capital respectively, to research venture capital portfolio's selection with considering inventors are disappointment aversion. Specifically, the main contents of this paper are as follows:At first, we use the Bayesian method to modify the estimated value of projects, and construct a single stage venture capital portfolio model based on the generalized disappointment models in Jia & Dyer(2001). Then, we generate projects' future values using the Monte Carlo stochastic simulation method to transfer the model into the deterministic optimization model, approximatively. The analysis of theory and simulation shows that the use of Bayes revised estimates in portfolio selection has a higher expected utility value in comparison with the straightforward portfolio selection based on ex ante value estimates, and the former can eliminate the expected gap between the realized ex post portfolio utility value and the estimated ex ante portfolio utility value, to reduce the amount of ex post disappointment that the venture capitalist may experience.Secondly, from the perspective of investment institutions, we consider about the mixed investment which includes securities and projects. Regarding venture capital as single stage investment, and regarding securities as multistage investment, we use the moment matching method to establish a single stage scenario generation model of the mixed investment portfolio's future returns, and build a mixture investment portfolio stochastic optimization model based on disappointment aversion. Finally, we use an example to describe the process that we establish the model, and the result shows that under the same risk tolerance or disappointment aversion level, the portfolio which contains projects will make investors get higher expected returns. In addition, the lower risk tolerance and the higher disappointment aversion level of the investors, the less expected return they will gain.Finally, the single stage mixed portfolio model is extended to the multistage model. Assuming that the price of security portfolio is fully determined by the current market status, projects' cash flows are only determined by the private status, we use the state tree to describe private and market' future states. Considering the investor is disappointment aversion, a multistage mixed investment portfolio model combining with projects' decision tree under uncertain environment is constructed. At the same time, based on the mixed investment portfolio optimization model, we give a method which can estimate projects' value. Following, a numerical example describes the process that using inverse optimization to solve the value of projects, and verifys the influence that capitalists' disappointment aversion psychological impacts on the investment decision.