Investment Optimization Model Based On Behavioral Finance Model

With the continuous development of social economy.The risks borne by financial institutions and investment individuals are increasing.The existed investment decision-making theory and optimized investment model can no longer formulistic explain the investment behavior of some investors in the financial market.For investors who are almost risk averse but risk loving at some wealth levels,we introduce the fractional degree reference dependent stochastic dominance theory and risk expectation dependence model,study how to establish a more reasonable and effective investment model.The main research content contains the following parts:The first chapter briefly introduces the development of stochastic dominance theory and risk expectation dependence model.The second chapter mainly studies the fractional degree reference dependent stochastic dominance.In order to solve the problem that the fractional stochastic dominance cannot distinguish the risky expectations,we introduce the fractional degree reference dependent stochastic dominance.Firstly,we provide it a simple and tractable equivalent integral condition based on the distribution function of the risk variable.Secondly,using probability transfers to explore the relationships between the fractional degree reference dependent stochastic dominance and the fractional degree stochastic dominance.Thirdly,we provide some sufficient conditions for the establishment order of fractional degree reference dependent stochastic dominance in the example of common distribution families,and some applications in the field of finance and insurance research of our stochastic dominance rules.Finally,considering the diversity of reference points,we take some random variables as reference points,and study their influence on investment behavior.The third chapter mainly studies the fractional degree expectation dependence.In order to provide a more accurate risk dependence model for investors who are almost risk averse but risk loving at some wealth levels,we extend the original integer-degree expectation dependence theory to the fractional degree.Firstly,to solve the problem that it is difficult to determine the utility function of investors in practical application,we establish an equivalent characterization based on the distribution function the fractional degree expectation dependence.Secondly,considering that financial derivatives are usually represented as a monotone increasing convexity transformation some primary assets in finance theory,we discuss the question whether fractional degree expectation dependence has invariance under monotone increasing concave transformation.Thirdly,we consider the uncertainty of investor preferences,and extend the fractional degree expectation dependence to the combine fractional degree expectation dependence.Finally,we apply the combine fractional degree expectation dependence model to the problem of investment diversification,and further extend the sufficient conditions to ensure the diversification of investment.The forth chapter summarizes the thesis and presents some shorting and future research.