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In this paper, we consider a trading algorithm for the investor with some prediction of the stock price in the market in order to gain excess returns, achieved by controlling the position of the stock held according to the prediction. We aim to find an optimal feedback control which maximizes the recursive mean-variance of the excess return. In this paper, we define the excess return to be the summation of every individual mean-variance for every operation. By mathematical induction, we generate an explicit expression of the different position lines, in terms of straight lines, corresponding to different signals in T + 0 market. Also, we prove that time-weighted average price (TWAP) strategy is the optimal strategy in T + 1 market when no information is available and present the numerical simulation for the kinked position lines in T + 1 market when prediction is possible. Particularly, we discover that the optimal feedback control, regardless of the type of market, is determined by all the straight or kinked position lines corresponding to all the different signals.

Optimal Position for Beating TWAP with Prediction in T + 0 and T + 1 Markets