Research On The Optimal Execution Strategy Of Investors Under Incomplete Information

In an idealized financial market,securities trading has sufficient liquidity,and investors can trade any share of securities immediately.However,in the real financial market,investors must face the adverse impact on security prices when conducting asset trading.At this time,investors need to minimize the adverse impact of buying and selling securities by formulating reasonable trading strategies.This paper studies the optimal execution strategies for investors with incomplete information.The investors know their trading goals,but they do not know the value of securities or trading information,so that then adjust their execution strategies based on the temporary impact of their trading on securities prices.This article first introduces the stochastic control problem,and deduces the Hamilton Jacobi Bellman equation based on the principle of dyna mic programming.Next,we propose five influencing factors that affect investors’ trading strategies,and establish the securities price fluctuation model with temporary and permanent impact,the optimal execution strategy model with maximum utility,the securities price fluctuation model under regime conversion,the securities price fluctuation model under the influence of other market traders,and the portfolio price fluctuation model under the influence of cross impact,repectively.Then the value equations of the models are transformed into solvable Hamilton-Jacobi-Bellman equation through dynamic programming principles.The analytical solution of the investor’s optimal execution strategy is obtained through simulation.Finally,the five models are numerically simulated to obtain thetrading strategies and intuitive numerical trading processes.The research results show that investors need to consider the impact of inventory penalties,operational penalties,utility functions,other traders in the market,and cross impact in asset groups when formulating an optimal execution strategy.By splitting a large trading order into multiple sub-orders to execute separatelly,the adverse effects of price shocks are reduced,and the expected returns of investors can be maximized.