Application of Operations Research Techniques in Trading

Trading involves a chain of decisions: which assets to hold, in what proportion, when to enter and exit, how much risk to accept, and which parameters should drive a rule-based signal. Operations Research (OR) treats each of these as a formal optimization problem with decision variables, constraints and an objective. This paper presents a comparative review of six studies that apply different OR methods to trading. Three address pair-based (statistical-arbitrage) trading: Majorization-Minimization for nonconvex mean-reverting portfolio design, optimal stopping for entry and exit timing, and bi-objective optimization for balancing profit against risk. The other three optimize the parameters of widely used technical indicators: exhaustive grid search for the MACD, a genetic algorithm for Bollinger Bands, and a two-stage genetic algorithm and artificial neural network for the Relative Strength Index (RSI). The comparison is qualitative, because the studies use different markets, periods, constraints and performance measures. The review finds that the method must be matched to the structure of the decision: nonconvex programming suits static allocation, stochastic control suits timing under uncertainty, multi-objective methods suit conflicting goals, and exhaustive or evolutionary search suits low-dimensional parameter tuning. Every method depends on assumptions that may not hold out of sample, so rigorous out-of-sample validation and explicit treatment of transaction costs are essential.