Market Inuence Of Portfolio Optimizers And Program Traders

The market influence caused by market participants on underlying prices of risky assets have received considerable attention in recent years,some scholars study that one economy which includes two types of investors,these of whom are reference traders and portfolio optimizers,but others focus on the other model economy consisting of two distinct groups of traders:reference traders and program traders.In this paper,We study one economy which includes three types of investors,they are reference traders,portfolio optimizers and program traders,which is really true in capital market. We analyze their market influence through mode ling, we first construct the refer-ence of Hamilton-Jacobi-Bellman equation,and conclude that the influence model of mar-ket with portfolio optimizers and program traders under their different demanding,then we establish another model with the market-clearing constraints and small parameters as-sumption,we gradually build up the model of market feedback effects under the demand of whom is a random variable,consequently,Ito formula and some mathematical skills are used to solve the solution of the related parameters of stochastic differential equation.We arrive at the explicit formulas for volatility of different traders,who have an effect on capital market,and the formula of expected return,and also the correction of investment scheme of portfolio optimizers,finally,It is found that portfolio optimizers influence the price of the risky asset so as to decrease its volatility,but program traders who increase the volatility of market which is uniform with a lot of papers who only consider two types of investors,however,we give the concrete expression of feedback effects,and analyze some results,there is good agreement between the numerical and analytical results when the wealth of the optimizers is so small,and also provide a theoretical basis and quantitative explanation for different investors in their bearing risk and making policy.