A Study On Optimization Model Of Multi-project Portfolio Based On Credibility Measure

Since Markowitz proposed the mean-variance model in1952, portfolio quantitativeresearch has been hot spot of the economic and financial theories. Traditional portfolioresearch mainly confined to financial markets. However, with the development of scientifictheory, the study of the modern portfolio gradually expanded to the financial market,including real estate, luxury goods, and the general project investment. With the globalizationof economic and the intensification of market competition, project portfolio is increasinglybecoming the hot topic in theory and in practice.Project investment is helpful for valuecreation, and to improve the economic strength and market competitiveness of investors.therefore, it is naturally favored by investors. In the real economy, whether individualinvestors or corporate investors will face many projects at the same time. If you chooseproperly, it will hinder the development of an individual or organization, or even will lead tocatastrophic loss.Since the uncertain future events cause different degrees of impact on theinvestment of investors, so investors are always in the process of investing in risk. Accordingto the definition of generalized risk, there are three kinds of the results of the risk to investors:loss, profit and no loss no profit. And the risk is objectivity, universality, loss and variability.Investors can only reduce the loss probability and loss magnitude and, but they cannotcompletely eliminate the risk.In conclusion, on the basis of previous studies, this paper is expanded from the followingaspects.Firstly, From the perspective of risk loss, we propose a multi-project portfolio decisionmodel with bankruptcy risk control. This model is based on the credibility measure theory.And according to the Roy’s definition, we obtain the mathematic formula of bankruptcy riskcontrol when the future cash flows are subject to the triangular fuzzy variables. Meanwhile,we use the genetic algorithm to solve our proposed model. A numerical example shows thatunder the same probability of bankruptcy, the lower living level, the higher expected return; atthe same living level, the higher the probability of bankruptcy, the higher expected return.Secondly, due to the market gain is often asymmetry, we consider the the profitability ofthe risk. According to the definition of skewness risk based on credibility measure theory, combining the fuzzy evaluation index of project investment, we obtain the fuzzy skewnessrisk index of project investment. In addition, this paper also introduce the risk-free asset tosolve the problem of effective use of the remaining funds. Based on the above, we propose amulti-project portfolio decision model with skewness risk control. we also use the geneticalgorithm to solve our proposed model. A numerical example shows that the objectivefunction value, total risk and total profits are basically increases with the increases ofminimum investment and the minimum skewness risk through controlling the parameters ofthe minimum investment and the minimum skewness risk.Thirdly, we investigate multi-project portfolio selection problem based on staffing.Assume that each project manager can only execute a project, each project can only becharged by a project manager, and they are independent of each other. This article, based onthe model of assignment problem and the theory of project investment, builds themulti-project portfolio model based on staffing and risk-free asset in fuzzy environment. Agenetic algorithm is given for solution. Through controlling the parameters of the minimuminvestment and the maximum risk tolerance, the numerical example shows that the objectivefunction value, total risk and total profits are increases with the increases of the maximum risktolerance, but they are increased first and declined with the increases of the minimuminvestment.In general, against the actual factors in project investment, we investigate multi-projectportfolio selection problem based on the credibility measure theory. This study not onlyenriches the modern portfolio theory, especially multi-project portfolio theory, but also hasimportant practical significance for multi-project portfolio.