Dynamic Programming and Optimal Lookahead Strategies in High Frequency Trading with Transaction Costs
25 Pages Posted: 3 Jan 2000
Date Written: October 1999
An optimal stochastic discrete time control problem with non smooth penalty function is considered. This problem naturally arises in high-frequency trading on financial markets. The principle of dynamic programming is formulated for this problem. Existence and uniqueness of the optimal strategy is proved. An algorithm for building a suboptimal strategy is presented and approximating properties of this strategy are studied. In addition, a simplified strategy is described which is a solution of an isotonic regression problem. A class of problems is defined on which this strategy can replace the basic suboptimal strategy. The results are illustrated by examples.
JEL Classification: C2, C53, C61, F17, F47
Suggested Citation: Suggested Citation