Variational Methods in Trading

Abstract

By and large, active market participants can be classified into two groups according to their trading strategies: those who trade contra-trend and those who follow the trend. Can these trading methods be justified theoretically? The answer is yes and variational methods play a crucial role. Here we illustrate how to justify the trend following trading strategy. We assume a regime switching market model and characterize the trading using a sequence of stopping times represent the actions of buy and sell. Optimizing a concave utility function we show that the optimal strategy is one that follows the trend characterized by the conditional probabilities of the bull market crossing two threshold curves. Tests using historical stock market illustrate how this trend following method work in actual markets. This talk is based on joint research with Min Dai (National University of Singapore) and Qing Zhang (Georgia State University at Athens).

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