PUBLICATIONS
There is nothing more practical than a good theory. Many models successfully applied in scientific fields are tremendously useful in addressing critical investment management problems. I have been fortunate enough to meet and work extensively with some of the leading figures in Pure Mathematics, Mathematical Finance, Machine Learning, Market Microstructure and Econometrics. The majority of our findings are kept proprietary. From time to time, however, we decide to publish some of them, hence the irregular frequency of the following publications.
RECENT PEERREVIEWED JOURNAL ARTICLES

AUTHORS 
TITLE 
REFERENCE 
INDEX 
SUMMARY 

Lopez de Prado, Marcos; Lewis, Michael 
Detection of False Investment Strategies Using Unsupervised Learning Methods 
Quantitative Finance. Forthcoming, 2019. 
JCR (IF = 1.170) 
In this paper we examine why false positives are so prevalent in finance, and we offer a practical solution to this industrywide problem. 

Risks,
Forthcoming. 2019. 
Growth Optimal Portfolio (GOP) theory determines the path of bet sizes that maximize longterm wealth. This multihorizon goal makes it more appealing among practitioners than myopic approaches, like Markowitz's efficient frontier. The GOP literature typically considers riskneutral investors with an infinite investment horizon. In this paper, we compute the optimal bet sizes in the more realistic setting of riskaverse investors with finite investment horizons. 


A Data Science Solution to the MultipleTesting Crisis in Financial Research 
Journal of Financial Data Science, 1(1), pp. 99110. 2019. 
Most discoveries in empirical finance are false, as a consequence of selection bias under multiple testing. We present a real example of how the adjusted false positive probability can be computed and reported for public consumption.  

Order from Chaos: How Data Science Is Revolutionizing Investment Practice 
Journal of Portfolio Management, 45(1), pp. 14. 2018. 
JCR (IF =
0.812) 
We describe some of the limitations of the econometrics toolkit, and how financial data science is helping overcome those limitations.  

Being Honest in Backtest Reporting: A Template For Disclosing Multiple Tests 
Journal of Portfolio Management, 45(1), pp. 141147. 2018. 
JCR (IF =
0.812) 
We propose a template that practitioners could use when pitching strategies to clients and senior management. By disclosing this information, those who are charged with making the final decision about a discovery can evaluate the probability that the purported discovery is false.  

Aparicio, Diego; Lopez de Prado, Marcos 
How Hard is to Pick the Right Model? 
Algorithmic Finance, 7(12), pp. 5361. 2018. 
MathSciNet; Zentralblatt MATH 
We evaluate the performance of the model confidence set (MCS) introduced in Hansen et al. (2011). We find that MCS is not robust to multiple testing and that it requires a very high signaltonoise ratio to discirimnate between true and false positives. 

The 10 Reasons Most Machine Learning Funds Fail 
Journal of Portfolio Management, 44(6), pp. 120133. 2018. 
JCR (IF =
0.812) 
The rate of failure in quantitative finance is high, and particularly so in financial machine learning. The few managers who succeed amass a large amount of assets, and deliver consistently exceptional performance to their investors. However, that is a rare outcome, for the reasons outlined in this paper.  

Bailey, David H.; Borwein, Jon M.; Salehipour, Amir; Lopez de Prado, Marcos  Evaluation and Ranking of Market Forecasters 
Journal of Investment Management, 16(2), pp. 4764. April 2018. 
We develop a novel ranking methodology to rank the market forecaster. In particular, we distinguish forecasts by their specificity, rather than considering all predictions and forecasts equally important, and we also analyze the impact of the number of forecasts made by a particular forecaster. We have applied our methodology on a dataset including 6,627 forecasts made by 68 forecasters. 


Machine Learning Funds and Investment Malpractice 
Oxford Business Law, March, 2018. 
Although there are no laws specifically prohibiting backtest overfitting (yet), investors may have a legal case against this widespread investment malpractice that professional associations of mathematicians have deemed unethical.  

Who needs a Newtonian Finance? 
Journal of Portfolio Management, 44(1), pp. 14. Fall 2017. 
JCR
(IF =
0.812) 
In this article, we discuss economics' obsession with calculus. Instead of focusing on that narrow topic, economics and finance students should be taught a much wider variety of mathematical subjects.  

Bailey, David H.; Borwein, Jon M.; Lopez de Prado,
Marcos; Zhu, Jim 
The Probability of Backtest Overfitting 
Journal of Computational Finance, 20(4), pp. 3970. 2017. 
JCR (5Y IF =
0.831) 
We propose a framework
that estimates the probability of backtest overfitting (PBO) specifically in
the context of investment simulations, through a numerical method that we
call combinatorially symmetric crossvalidation (CSCV). We show that CSCV
produces accurate estimates of the probability that a particular backtest is
overfit. 

Finance as an Industrial Science 
Journal of Portfolio Management, 43(4), pp. 59. Summer 2017. 
JCR (IF = 0.812)  Finance cannot become a rigorous science (in the Popperian or Lakatosian sense), however it can still operate as an “industrial science”. This article describes the scientific method by which industrial finance discovers through experimentation, and avoids false discoveries.  

Stock portfolio design and backtest overfitting 
Journal of Investment Management, 15(1), pp.113. 2017. 
We demonstrate a computer program that designs a portfolio consisting of common securities, such as the constituents of the S&P 500 index, that achieves any desired profile via insample backtest optimization. These portfolios typically perform erratically on more recent, outofsample data, which is symptomatic of selection bias. One implication of these results is that socalled smart beta funds, which are designed insample to deliver a desirable performance pro file, are likely to disappoint outofsample. 


Rosenberg, Gili; Poya Haghnegahdar; Goddard, Phil; Lopez de Prado, Marcos; Carr, Peter; Wu, Kesheng 
Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer 
IEEE Journal of Selected Topics in Signal Processing, 10(6), pp. 10531060. September 2016. 
JCR (IF =
4.361) 
We solve a multiperiod portfolio optimization NPcomplete problem using DWave's quantum annealer. The formulation incorporates transaction costs (including permanent and temporary market impact) and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multiperiod portfolio optimization problem we solve is significantly harder than the continuous variable problem. 

Mathematics and Economics: A reality check 
Journal of Portfolio Management, 43(1), pp. 58. Fall 2016. 
JCR (IF = 0.812)  Economics (and by extension finance) is arguably one of the most mathematical fields of research. However, economists’ choice of math may be inadequate to model the complexity of social institutions. In a constructive spirit, this note offers some advice on how students could increase their chances of having a successful career in 21st century finance. Practitioners seeking to enhance their skillset may also draw some ideas.  

Journal of Investing, 25(3), pp. 142154. Fall 2016. 
We introduce Kinetic Component Analysis (KCA), a
statespace application that extracts the signal from a series of noisy
measurements by applying a Kalman Filter on a Taylor expansion of a
stochastic process. We show that KCA presents several advantages compared to
other popular noisereduction methods such as Fast Fourier Transform (FFT) or
Locally Weighted Scatterplot Smoothing (LOWESS). 


Building Diversified Portfolios that Outperform OutOfSample 
Journal of Portfolio Management, 42(4), pp. 5969. Summer 2016. 
JCR (IF = 0.812)  HRP portfolios address three major concerns of quadratic optimizers in general and Markowitz’s CLA in particular: Instability, concentration and underperformance. Monte Carlo experiments show that HRP delivers lower outofsample variance than CLA, even though minimumvariance is CLA’s optimization objective. HRP also produces less risky portfolios outofsample compared to traditional risk parity methods.  

Quantitative Finance, 16(8), pp. 11751176, 2016. 
JCR (IF = 1.170) 
A review of the monograph recently published by Cambridge
University Press. 

Journal of Financial Economics, 120(2), pp. 269286. May 2016. 
JCR (5Y IF = 7.513)  We examine the accuracy of three methods for classifying trade data: Bulk Volume Classification (BVC), Tick Rule and Aggregated Tick Rule. We develop a Bayesian model of inferring information from trade executions, and show that BVC has the highest explanatory power over the bidask spread.  

Bailey, David H.; Borwein, Jon M.;
Salehipour, Amir; Lopez de Prado,
Marcos; Zhu, Jim 
Backtest Overfitting in Financial Markets 
Automated Trader, Issue 39. Spring 2016. 
We introduce two online backtest overfitting tools: BODT simulates the overfitting of seasonal strategies (typical of technical analysis), and TMST simulates the overfitting of econometric strategies (typical of academic journals). We show that econometric methods lend themselves to extreme levels of overfitting, casting doubt on most investment strategies published in academic journals.  

StopOuts Under Serial Correlation and "The Triple Penance Rule" 
Journal of Risk, 18(2), pp. 6193. Fall 2015. 
JCR (5Y IF =
1.794) 
We develop a framework for informing the decision of stopping a portfolio manager or investment strategy once it has reached a loss or time under water limit for a certain confidence level. Under standard portfolio theory assumptions, we show that it takes three times longer to recover from the expected maximum drawdown than the time it takes to produce it, with the same confidence level. Mathematical Appendices available here. 


Journal of Portfolio Management, 42(1), pp. 2933. Fall 2015. 
JCR (IF = 0.812)  Financial economics is a surprisingly prolific, topic redundant, asocial field, where most papers go largely ignored. Author collaboration improves scientific output, and yet financial economics seems to be one of the least cooperative empirical fields. If these trends continue, financial economics may be in the path to become a pathological science, a collection of “cold fusion” claims.  

Mathematical Finance, 25(3), pp. 640672. July 2015. 
JCR (IF = 2.714) 
Execution traders know that market impact greatly depends
on whether their orders lean with or against the market. And yet, the
literature on optimal execution strategies rarely incorporates order
imbalance in the modeling of transaction costs. We introduce the OEH model,
which considers this fact when determining the optimal trading horizon for an
order, an input required by many sophisticated execution strategies. 


Journal of Portfolio Management, 41(4), pp. 140144. Summer 2015. 
JCR (IF = 0.812)  Empirical Finance is in crisis: Our most important discovery tool is historical simulation, and yet, most backtests and time series analyses published in journals are flawed. The problem is wellknown to professional organizations of Statisticians and Mathematicians, who have publicly criticized the misuse of mathematical tools among Finance researchers. In this note I point to three problems and propose four practical solutions. An interview on this research appeared in IIJ's Practical Applications (Winter 2016).  

Practical
Applications, Institutional Investor Journals, 2(3),
pp. 13, Winter 2014. 
Quantitative MetaStrategies (QMS) are quantitative strategies designed to manage investment strategies. As a field, QMS can be defined as the mathematical study of the decisions made by the supervisor of a team of investment managers, regardless of whether their investment style is systematic or discretionary. 


Bailey, David H.; Borwein,
Jon M.; Lopez de Prado, Marcos; Zhu, Jim 
Notices of the
American Mathematical Society, 61(5), pp. 458471. May 2014. 
We prove that high simulated performance is easily
achievable after backtesting a relatively small number of alternative
strategy configurations, a practice we denote “backtest overfitting”. Because
financial analysts rarely report the number of configurations tried for a
given backtest, investors cannot evaluate the degree of overfitting in most
investment proposals. This is one of the first Mathematical Finance papers
published in the Notices of the AMS, the official membership journal of
the American Mathematical Society. 


A
Mixture of Gaussians Approach to Mathematical Portfolio Oversight: The EF3M
Algorithm

Quantitative Finance, 14(5), pp. 913930. 2014 
JCR (IF = 1.170) 
We solve the "Nonic Polynomial problem" posed by Karl Pearson in the 1894 edition of the Philosophical Transactions of the Royal Society.
We apply quantitative methodologies originated in the Mathematical Theory of
Evolution to model the dynamics of investment styles within a fund. 


The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting and NonNormality 
Journal of
Portfolio Management,
40 (5), pp. 94107. 2014 (40th Anniversary Special Issue) 
JCR (IF = 0.812) 
The Deflated Sharpe Ratio (DSR) corrects for two
leading sources of performance inflation: Selection bias under multiple
testing and nonNormally distributed returns.
In this interview,
Prof. Bailey speaks about our work.
IIJ's Practical Applications (Winter 2015) featured this work. Other authors in this JPM Special Issue include: Cliff Asness (AQR), John Bogle (Vanguard), Mohamed ElErian (Allianz), Robert Kapito (BlackRock), Mark Kritzman (Windham), Martin Leibowitz (Morgan Stanley), Burton Malkiel (Princeton) and Marc Reinganum (State Street). 


Algorithmic Finance,
3(1), pp. 2142. 2014. 
We introduce Stochastic Flow Diagrams (SFDs), a new
mathematical approach to represent complex dynamic systems into a single
weighted digraph. This topological representation provides a way to visualize
what otherwise would be a morass of equations in differences. 

Song, Jung H.; Lopez de Prado, Marcos; Simon, Horst D.; Wu, Kesheng 
Exploring Irregular Time Series Through the NonUniform Fourier Transform  Proceedings of the International Conference for High Performance Computing, IEEE, 2014.  We explore the frequency domain of irregular time series by applying a NonUniform Fast Fourier Transform (NUFFT) on Natural Gas Futures prices. We show that HighFrequency Traders are responsible for a growing number of cyclical patterns. In particular, we observe the emergence of a new power law in the Fourier spectra in recent years.  

Journal of Financial Markets,
17(1), pp. 4752. 2014. 
JCR (5Y IF =
2.234) 
Discusses implementation cautions with regards to VPIN
empirical studies. 


The Topology of Macro Financial Flows: An Application of
Stochastic Flow Diagrams 
Algorithmic Finance,
3(1), pp. 4385. 2014. 
We construct a network of financial instruments and show
how Stochastic Flow Diagrams (SFDs) allow researchers to monitor the
flow of capital across the financial system. Because our approach is dynamic,
it models how and for how long a financial shock propagates through the
system. 


An OpenSource implementation of the
CriticalLine Algorithm for Portfolio Optimization 
Algorithms, 6(1), pp. 169196. 2013. 
We fill a gap in the literature by providing a
welldocumented, stepbystep opensource implementation of the CriticalLine
Algorithm (CLA) in a scientific language. We discuss the logic behind CLA
following the algorithm’s decision flow. In addition, we have developed
several utilities that facilitate the answering of recurrent practical
problems. 


The Strategy Approval Decision: A Sharpe Ratio
Indifference Curve Approach 
Algorithmic Finance,
2(1), pp. 99109. 2013. 
The problem of capital allocation to a set of strategies could be partially avoided, or at least greatly simplified, with an appropriate strategy approval decision process. This paper proposes such procedure, by splitting the capital allocation problem into two sequential stages: Strategy approval and portfolio optimization. 


Journal of Risk, 15(2), pp. 344, Winter. 2012. 
JCR (5Y IF =
1.794) 
Introduced the Probabilistic Sharpe Ratio (PSR), a new uncertaintyadjusted investment skill metric that corrects the inflationary effect that NonNormality has on Sharpe Ratio estimates. It also determines the Minimum Track Record Length (MinTRL) needed to evidence skill. A Sharpe Ratio Efficient Frontier (SEF) arises, based on returnonrisk rather than returnoncapital. 


Balanced Baskets: A new approach to Trading and Hedging
Risks 
Journal of Investment Strategies,
1(4), pp. 2162. Fall, 2012. 

Introduced the notion of Balanced Baskets, which are portfolios of instruments that evenly spread risks or exposures across their constituents without requiring a change of basis, like PCA. It also developed the algorithms needed to compute such baskets in hedging as well as trading applications. Finally, it also contributed a new procedure for covariance clustering. 


Journal of Portfolio Management,
39(1), pp. 1929. Fall, 2012. 
JCR (IF = 0.812) 
This paper has been cited by Market Regulators [1, 2, 3] for deepening their understanding of the phenomenon of High Frequency Trading (HFT), beyond the simple notion of "speed trading". In particular, it argues that at the heart of HFT is a new investment paradigm based on making decisions in Volume Time. IIJ's Practical Applications (Fall 2013) featured this work. 


Review of Financial Studies, 25(5), pp. 14571493. 2012. 
JCR (5Y IF = 5.864) 
Developed a new procedure to estimate the flow toxicity
impacting market makers, the Volume Synchronized Probability of Informed
Trading (VPIN). This metric has been shown to
anticipate liquidity crises (including the Flash Crash) and to be a good
predictor of toxicityinduced volatility. CFTC's HFT guidelines
cite this publication. 


Advances in Cointegration and Subset Correlation Hedging
Methods 
Journal of Investment Strategies,
1(2), pp. 67115. Spring, 2012. 

Introduced two new hedging methods, called DickeyFuller Optimization (DFO) and MiniMax Subset Correlation (MMSC). The former is a dynamic, cointegration based method while the latter is a static, balancedbasket method to evenly distribute exposure among portfolio constituents. It also generalized the BoxTiao Canonical Decomposition (BTCD) method. 


Journal of Trading,
6(2), pp. 813. Spring, 2011. 

It introduced the concept of "Market Makers' Asymmetric Payoff Dilemma", which characterizes a liquidity provider as the seller of a realoption to be adversely selected. Since that option cannot be dynamically replicated, a new contract is proposed to allow market makers to hedge such risks. 


Journal of Portfolio Management,
37(2), pp. 118128. Winter, 2011. 
JCR (IF = 0.812) 
This has become one of the most read papers in Finance, according to SSRN. It analyses the "Flash Crash" from a microstructure perspective, and concludes that it was a liquidity crises which resulted from market makers receiving persistently toxic order flow for at least 2 hours before the crash actually unfolded. 


Journal of Alternative
Investments, 7(1), pp. 731. Summer, 2004. 

It developed a new risk framework for assessing hedge funds' loss potential, considering NonNormal and SeriallyCorrelated returns. It shows that the IID Normal assumption, ubiquitous in financial risk modeling, leads to a great underestimation of the loss potential of hedge funds. 
PEERREVIEWED ACADEMIC BOOKS

AUTHORS 
TITLE 
REFERENCE 
NOTABLE
INNOVATION 

Lopez de Prado, Marcos  Machine Learning for Financial Researchers  Cambridge University Press, forthcoming 2019.  The purpose of this monograph is to introduce ML tools that are useful for discovering economic and financial theories. Successful investment strategies are specific implementations of general theories. An investment strategy that lacks a theoretical justification is likely to be false. Hence, a researcher should concentrate her efforts on developing a theory, rather than of backtesting potential trading rules. 

Lopez de Prado, Marcos  Advances in Financial Machine Learning  Wiley, 2018.  Machine learning (ML) is changing virtually every aspect of our lives. Today ML algorithms accomplish tasks that until recently only expert humans could perform. As it relates to finance, this is the most exciting time to adopt a disruptive technology that will transform how everyone invests for generations. 

Lopez de Prado, Marcos (Ed.)  Special Guide to Applied Data Sciences in Finance  Journal of Investing, Vol. 25(3), pp.69159. 2016  Today, scientists model financial markets as true complex dynamic systems, applying methodologies borrowed from all areas of science and engineering. Whether it is signal processing, network analysis or data visualization, modern methods can help us answer fundamental questions that traditional econometric methods have failed to tackle over decades. Coauthors include: Stephen Boyd, Riccardo Rebonato, Phil Goddard, Thomas Wiecki and Jessica Stauth. 

Bailey, David H.; Ger, Stephanie; Lopez de Prado, Marcos; Sim, Alexander; Wu, Kesheng  Statistical Overfitting and Backtest Performance, in RiskBased and Factor Investing  Quantitative Finance Elsevier, 2016.  This book (edited by Emmanuel Jurczenko) is a compilation of recent articles written by leading academics and practitioners in the area of riskbased and factor investing (RBFI). The articles are intended to introduce readers to some of the latest, cutting edge research encountered by academics and professionals dealing with RBFI solutions. Together the authors detail both alternative nonreturn based portfolio construction techniques and investing style risk premia strategies. 

Easley, David; 
High Frequency Trading: New Realities for
Traders, Markets and Regulators 
Risk
Books, 2013. 
An overview of high frequency trading (HFT) strategies,
with a particular focus on how low frequency traders can survive in a high
frequency world. Contributors include leading practitioners and academics in this field: Robert Almgren (Quantitative Brokers, New York University), Wes Bethel (Lawrence Berkeley National Laboratory), Ming Gu (Lawrence Berkeley National Laboratory), Terry Hendershott (U.C. Berkeley), Charles Jones (Columbia University), Michael Kearns (S.A.C. Capital, University of Pennsylvania), David Leinweber (Lawrence Berkeley National Laboratory), Oliver Linton (University of Cambridge), Albert Menkveld (University of Amsterdam), Yuryi Nevmyvaka (University of Pennsylvania), Richard Olsen (Olsen Ltd.), Oliver Ruebel (Lawrence Berkeley National Laboratory), George Sofianos (Goldman Sachs), Michael Sotiropoulos (Bank of America Merrill Lynch), Kesheng Wu (Lawrence Berkeley National Laboratory), and JeanPierre Zigrand (London School of Economics). 

Complutense University, 2011. 
This is the author's second doctoral dissertation. The
generalization of electronic markets and ubiquitous automation of financial
transactions has rendered many established models and theories obsolete. This
work presents a new scientific framework for the study of some of the most
relevant questions concerning High Frequency Trading. 


Díaz de Santos,
2003. 
This is the author's first doctoral dissertation, which
dealt with portfolio optimization, risk management and capital allocation to
hedge funds. Once hedge funds' hidden risks are taken into account, optimal
allocations are much smaller than proposed by the standard Markowitz
approach. 
WORKING PAPERS AND BOOKS
AUTHORS 
YEAR 
TITLE 
NOTABLE
INNOVATION 
2019 
Beyond Econometrics: A Roadmap Towards Financial Machine Learning 
This article demonstrates that each analytical step of the econometric process has a homologous step in ML analyses. By clearly stating this correspondence, my goal is to facilitate and reconcile the adoption of ML techniques among econometricians. 

2019 
This article describes ten notable financial applications where ML has moved beyond hype and proven its usefulness. This success does not mean that the use of ML in finance does not face important challenges. The main conclusion is that there is a strong case for applying ML to current financial problems, and that financial ML has a promising future ahead. 

Bailey, David H.; Borwein, Jon M.; Salehipour, Amir; Lopez de Prado, Marcos 
2019 
This study develops a novel ranking methodology to rank market forecasters. In particular, we distinguish forecasts by their specificity, rather than considering all predictions and forecasts equally important, and we also analyze the impact of the number of forecasts made by a particular forecaster. We have applied our methodology on a dataset including 6,627 forecasts made by 68 forecasters. 

2018 
The False Strategy Theorem: A Financial Application of Experimental Mathematics 
We estimate the expected value of the maximum Sharpe ratio as a function of the number of trials. Through experimental mathematics, we evaluate the accuracy of the estimate. The implication is that there is no Sharpe ratio threshold above which we may reject the hypothesis that a strategy is false. With enough number of trials, any false strategy may achieve a Sharpe ratio as high as a researcher demands. 

Lopez de Prado, Marcos; Lewis, Michael J. 
2018 
Confidence and Power of the Sharpe Ratio under Multiple Testing 
Most papers in the financial literature estimate the pvalue associated with an investment strategy, without reporting the power of the test used to make that discovery. In this paper we provide analytic estimates to Type I and Type II errors for the Sharpe ratios of investments, and derive their familywise counterparts. These estimates allow researchers to carefully design experiments with high confidence and power. 
Song, Jung H.; Lopez de Prado, Marcos; Simon, Horst D.; Wu, Kesheng 
2015 
Intraday Patterns in Natural Gas Futures: Extracting Signals from HighFrequency Trading Data 
As algorithms replace an increasing number of tasks previously performed by humans, cascading effects similar to the Flash Crash of May 6th 2010 become more likely. A case in point are the impact of weather forecasts on Natural Gas trading. The Fourier components corresponding to high frequencies are becoming more prominent in the recent years and are much stronger than could be expected from the structure of the market. 
Bailey, David H.; Borwein, Jon M.;
Salehipour, Amir; Lopez de Prado,
Marcos; Zhu, Jim 
2015 
Backtest Overfitting Demonstration Tool: An Online Interface 
In this study we introduce two online tools, the Backtest Overfitting Demonstration Tool, or BODT for short, and the Tenure Maker Simulation Tool, or TMST, which illustrate the impact of backtest overfitting on investment models and strategies. We describe BODT and TSMT, the experiments they perform, together with technical details such as the evaluation metrics and parameters used. 
2015 
Generalized Optimal Trading Trajectories: A Financial Quantum Computing Application 
Generalized dynamic portfolio optimization problems have no known closedform solution. These problems are particularly relevant to large asset managers, as the costs from excessive turnover and implementation shortfall may critically erode the profitability of their investment strategies. In this brief note we demonstrate how this financial problem, intractable to modern supercomputers, can be reformulated as an integer optimization problem. Such representation makes it amenable to quantum computers. 

2014 
We present empirical evidence of the existence of optimal trading rules (OTRs) for the case of prices following a discrete OrnsteinUhlenbeck process, and show how they can be computed numerically. Although we do not derive a closedform solution for the calculation of OTRs, we conjecture its existence on the basis of the empirical evidence presented. Also available in ArXiv. 