Dynamic Programming and Optimal Lookahead Strategies in High Frequency Trading with Transaction Costs

25 Pages Posted: 3 Jan 2000

Date Written: October 1999

Abstract

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

Vigodner, Alexander, Dynamic Programming and Optimal Lookahead Strategies in High Frequency Trading with Transaction Costs (October 1999). Available at SSRN: https://ssrn.com/abstract=192848 or http://dx.doi.org/10.2139/ssrn.192848

Alexander Vigodner (Contact Author)

Bloomberg Financial Markets (BFM) ( email )

IBM-house 10th floor
32 Weizmann Street
Tel Aviv, 61336
Israel

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