Numerical methods for buying-low-and-selling-high stock policy

This work develops numerical methods using stochastic approximation approach for an optimal stock trading (buy and sell) strategy. Assuming the underlying asset price is governed by a mean-reverting stochastic process, we aim to find buying and selling strategies so as to maximize an overall expected return. One of the advantageous of our approach is that the underlying asset is model free. Only mean reversion is required. Slippage cost is taken into consideration for each transaction. Convergence of the algorithms is provided. Numerical examples are reported to demonstrate the results.