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Trading Strategies with Position Limits

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  • Valerii Salov

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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  • Valerii Salov, 2017. "Trading Strategies with Position Limits," Papers 1712.07649, arXiv.org.
    • Handle: RePEc:arx:papers:1712.07649
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    References listed on IDEAS

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    1. Valerii Salov, 2013. "Optimal Trading Strategies as Measures of Market Disequilibrium," Papers 1312.2004, arXiv.org.
    2. Valerii Salov, 2015. "The Role of Time in Making Risky Decisions and the Function of Choice," Papers 1512.08792, arXiv.org.
    3. Neftci, Salih N, 1991. "Naive Trading Rules in Financial Markets and Wiener-Kolmogorov Prediction Theory: A Study of "Technical Analysis."," The Journal of Business, University of Chicago Press, vol. 64(4), pages 549-571, October.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. Goodhart, Charles A. E. & O'Hara, Maureen, 1997. "High frequency data in financial markets: Issues and applications," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 73-114, June.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    8. Hirsa, Ali & Neftci, Salih N., 2013. "An Introduction to the Mathematics of Financial Derivatives," Elsevier Monographs, Elsevier, edition 3, number 9780123846822.
    9. Valerii Salov, 2017. "The Wandering of Corn," Papers 1704.01179, arXiv.org.
    10. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
    11. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
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