Trading Strategies with Position Limits
Valerii Salov

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.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Stochastic processes and financial applications
