Trading Strategies with Position Limits

TL;DR

This paper analyzes trading strategies constrained by position limits, deriving formulas for strategy counts, distributions, and properties, and explores algebraic structures and optimal patterns for maximizing profit.

Contribution

It introduces a mathematical framework for finite trading strategies with position limits, including formulas, distributions, and algebraic properties, advancing understanding of strategy structure.

Findings

Formulas for number of strategies and transactions

Distribution and moments of trading actions

Algebraic properties of strategy spaces

Abstract

Whether you trade futures for yourself or a hedge fund, your strategy is counted. Long and short position limits make the number of unique strategies finite. Formulas of the numbers of strategies, transactions, do nothing actions are derived. A discrete distribution of actions, corresponding probability mass, cumulative distribution and characteristic functions, moments, extreme values are presented. Strategies time slice distributions are determined. Vector properties of trading strategies are studied. Algebraic not associative, commutative, initial magmas with invertible elements control trading positions and strategies. Maximum profit strategies, MPS, and optimal trading elements can define trading patterns. Dynkin introduced the term interpreted in English as "Markov time" in 1963. Neftci applied it for the formalization of Technical Analysis in 1991.