A Portfolio Optimization Problem Based On Belief-Dependent Utility In Ambiguous Situations

With the rapid development of the market economy and frequent market fluctuations,the complexity of the current market makes investors face more and more complex and uncertain theoretical and practical problems in financial investment decisions,and diversified research on portfolio optimization problems is becoming more and more of great practical significance.Due to the shackles of traditional finance,there is no clear understanding of the attitude of investors,at the time,investors have a strong subjective initiative,its changes are very complex,how to portray it is also a problem,it is affected by many factors.Ambiguous attitudes under uncertainties play an important role in decision-making,and although it is difficult to measure,many theoretical models in specific situations have been proposed in the research of many scholars at home and abroad.At present,the problem of portfolio selection is affected by multiple factors,and the developed theoretical model is increasingly not applicable to complex and changeable practical situations,and the subjective influence of investors plays a large role.The optimization problem is based on the principle of utility maximization,which believes that the result depends not only on the choice of behavior,but also on random changes in the state itself.This paper first proposes a general behavioral portfolio selection model,which is different from the traditional maximum and minimum decision-making model,introducing ambiguity in the form of double expectation,adding the ambiguous attitude of investors to the model,emphasizing the impact of ambiguity on investment strategy,introducing subjective probability distribution,and taking uncertainty as uncertainty between probability distributions of different outcomes.Investors use the classical hierarchy-dependent utility model theory for the valuation of utility functions under risk conditions,which has a utility(value)function and a probability distortion function of S shape.The ultimate goal is to maximize the ultimate wealth,thereby maximizing the expected utility.By solving the optimal investment ratio under different utility function forms and different distributions,the impact of introducing fuzzy situations on portfolio selection is analyzed,and the traditional maximum and minimum decision models are compared and concluded.The results show that investors’ attitude towards ambiguity has had an impact on investment strategies.