Investigations On The Evolution Of Investment Decision-making Based On Boltzmann Equation

Our research is based on the theory of rarefied gas dynamics and the assumption of bounded rationality.This dissertation takes compromise psychology as one of the variables that affect investment decision-making,and sets up an investment decision-making model with the risk tolerance as the independent variable to study how a group of investors can reach a consensus.Specifically,this dissertation approaches the issue from the following three aspects:(1)In Chapter 2,according to the rarefied gas dynamics theory,investors are regarded as coarse grained molecules in the thin air,and the dynamic models of the investor's risk tolerance are set according to the dynamic model of molecular energy exchange.The degree of compromise is one of the independent variables in the investment decision-making model,in which the risk tolerance determines the degree of willingness to compromise.Through the compromise function,investor's risk tolerance is linked to the investment decision.As a result,the evolution model of the investment decision is embedded with the evolution model of the risk tolerance,and an investment-decision model that depends on the risk tolerance is established.The risk tolerance and investment decisions are dynamic variables that change over time,and their changing rules are defined by dynamic models.After the model is set up,we discuss the dynamic process of the risk tolerance and obtained its steady state solution,which proves that the risk tolerance converges to a certain fixed value.Compromise is a decreasing function of the risk tolerance.The higher the risk tolerance is,the higher the corresponding metacognitive ability and the more objective the self understanding will be.Each investor has two identification variables: the risk tolerance and investment decision.The Boltzmann equation is used to describe the changes in investor density distribution over time,and the corresponding Fokker-Planck equation is derived through the progressive method and the stability of investment decision-making is obtained.The state solution indicates that the investment decision converges to this fixed value.Through Monte Carlo simulation of the evolution process,it is concluded that the lower the investor's risk tolerance is,the higher the possibility and degree of compromise,and the greater the investor's influence from other investors will be.The simulation also proves the research conclusion of social psychologists who point out that another important factor affecting consistency is the number of people holding a certain decision.The greater the number is,the attractiveness of this decision to other investors will be stronger.(2)When there is manager influence,investors not only need to consider the decisions of other investors around them,but also need to complete decision-making tasks in accordance with the goals of manager.Chapter 3discusses one type of manager's influence,namely a request from manager,requiring investors to make any consistent decision for a complex investment project,and to penalize investors who are too stubborn or refuse to cooperate.Then,investors should refer to the opinions of other investors and make more compromises and concessions.Since manager only require consensus,and did not make specific requirements for which consensus decision is,we find that the final investment decision has an important relationship with the initial decision state.In the process of mathematical modeling,manager's influence is described by adding control items to the system.According to the special objective of manager in this chapter,the control items satisfy a cost function that minimizes the difference between the decisions of all investors.After performing mathematical calculations and simulation experiments on the decision-making model,we point out that under the supervision of manager,investors will realize a stronger sense of cooperation in order to achieve consensus,make decisions faster to reach consensus,and the unity of investors higher.(3)Chapter 4 is about the investment decision-making research of large groups.When the number of investors is large,they are divided into leader groups and follower groups according to their risk tolerance.Leaders use certain leadership strategies to lead investors to reach a certain expected consensus.According to the different subjects of the interaction,three investment decision making models are to be given: leader-leader decision making model,follower-follower decision making model,and follower-leader decision making model.In fact,the investment decision of the leader will not be influenced by the investment decision of the follower.The leader has much more resources and information than the follower,and the leader will only use the decisions of other leaders as a reference.The followers not only need to consider the decision of the leader,but also be influenced by the decisions of other investors.In mathematical modeling,a specific control item is used to describe the leadership strategy.The cost function that the control item needs to meet is: minimize the difference between the target consensus specified by the investors and the leader,and at the same time,the follower's average decision of previous period influences the leader's strategy of next period.After the investment decision making model is set up,mathematical calculations and simulations are performed on the leader's decision making evolution and the follower's decision making evolution.The results show that the size of the leader's control role and the different control strategies will cause investors to gather in different decisions.