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On Performance Limits of Feedback ControlBased Stock Trading Strategies
 in Proceedings of the 2011 American Control Conference
, 2011
"... Abstract — The starting point for this paper is the control theoretic paradigm for stock trading developed in [1]. Within this framework, a socalled idealized market is characterized by continuous trading and smooth stock price variations. Subsequently, a feedback controller processes the stock pri ..."
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Abstract — The starting point for this paper is the control theoretic paradigm for stock trading developed in [1]. Within this framework, a socalled idealized market is characterized by continuous trading and smooth stock price variations. Subsequently, a feedback controller processes the stock price history p(t) to determine the current level of investment I(t). In this idealized setting, we show that feedback control laws exist which guarantee a profit for all admissible price variations. This first result is only viewed as a benchmark because the controller which achieves this trading profit relies on price signal differentiation which is undesirable. Subsequently, the paper concentrates on more practical differentiatorfree controller dynamics. For the simple case of a static linear feedback on the cumulative trading profit or loss g(t), surprisingly, it turns out that a profit is still guaranteed. The final part of the paper involves numerical simulation using historical price; we study the extent to which the idealized market results carry over to real markets. I.
Market making and mean reversion
 In Proc. ACM Conf. on Elec. Commerce
, 2011
"... Market making refers broadly to trading strategies that seek to profit by providing liquidity to other traders, while avoiding accumulating a large net position in a stock. In this paper, we study the profitability of market making strategies in a variety of time series models for the evolution of a ..."
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Market making refers broadly to trading strategies that seek to profit by providing liquidity to other traders, while avoiding accumulating a large net position in a stock. In this paper, we study the profitability of market making strategies in a variety of time series models for the evolution of a stock’s price. We first provide a precise theoretical characterization of the profitability of a simple and natural market making algorithm in the absence of any stochastic assumptions on price evolution. This characterization exhibits a tradeoff between the positive effect of local price fluctuations and the negative effect of net price change. We then use this general characterization to prove that market making is generally profitable on mean reverting time series — time series with a tendency to revert to a longterm average. Mean reversion has been empirically observed in many markets, especially foreign exchange and commodities. We show that the slightest mean reversion yields positive expected profit, and also obtain stronger profit guarantees for a canonical stochastic mean reverting process, known as the OrnsteinUhlenbeck (OU) process, as well as other stochastic mean reverting series studied in the finance literature. We also show that market making remains profitable in expectation for the OU process even if some realistic restrictions on trading frequency are placed on the market maker.
On Arbitrage Possibilities Via Linear Feedback in an Idealized Brownian Motion Stock Market
"... Abstract — This paper extends the socalled Simultaneous LongShort (SLS) linear feedback stock trading analysis given in [2]. Whereas the previous work addresses a class of idealized markets involving continuously differentiable stock prices, this work concentrates on markets governed by Geometric ..."
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Abstract — This paper extends the socalled Simultaneous LongShort (SLS) linear feedback stock trading analysis given in [2]. Whereas the previous work addresses a class of idealized markets involving continuously differentiable stock prices, this work concentrates on markets governed by Geometric Brownian Motion (GBM). For this class of stock price variations, the main results in this paper address the extent to which a positive trading gain g(t)> 0 can be guaranteed. We prove that the SLS feedback controller possesses a remarkable robustness property that guarantees a positive expected trading gain E[g(t)]> 0 in all idealized GBM markets with nonzero drift. Additionally, the main results of this paper include closed form expressions for both g(t) and its probability density function. Finally, the use of the SLS controller is illustrated via a detailed numerical example involving a large number of simulations. I.
Bargaining and Pricing in Networked Economic Systems
, 2011
"... Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, w ..."
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Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, we model an economic system as a combination of many bilateral economic opportunities, such as that between a buyer and a seller. The transactions are complicated by the existence of many economic opportunities, and the influence they have on each other. For example, there may be several prospective sellers and buyers for the same item, with possibly differing costs and values. Such a system may be modeled by a network, where the nodes represent players and the edges represent opportunities. We study the effect of network structure on the outcome of bargaining among players, through theoretical
On MarketNeutral Stock Trading Arbitrage Via Linear Feedback
"... Abstract — This paper develops a new version of the socalled Simultaneous LongShort (SLS) linear feedback stock trading controller for a class of idealized markets characterized by continuously differentiable stock prices. The two salient features of our new controller are as follows: First, all t ..."
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Abstract — This paper develops a new version of the socalled Simultaneous LongShort (SLS) linear feedback stock trading controller for a class of idealized markets characterized by continuously differentiable stock prices. The two salient features of our new controller are as follows: First, all trading gains are appropriately discounted to account for “opportunity costs” associated with an alternative investment in a riskfree bond. Second, the new feedback control strategy provides the investor with flexibility to obtain trading gains which are decoupled from the market behavior at large; i.e., a certain “market neutrality condition ” is satisfied. The issue of arbitrage is the focal point of this paper. That is, even if interest rate discounting of trading gains is considered, whether the market goes up or down, the account value V(t) will exceed its initial value V(0) for all nontrivial stock price variations. In recognition of the fact that the idealized market only serves as a benchmark indicating the “realm of possibilities ” for a real market, we also include numerical simulations indicating the performance of the controller using realworld historical prices. I.
Dynamic Spread Trading
, 2008
"... This paper is concerned with a dynamic trading strategy, which involves multiple synthetic spreads each of which involves long positions in a basket of underlying securities and short positions in another basket. We assume that the spreads can be modeled as meanreverting OrnsteinUhlenbeck (OU) pro ..."
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This paper is concerned with a dynamic trading strategy, which involves multiple synthetic spreads each of which involves long positions in a basket of underlying securities and short positions in another basket. We assume that the spreads can be modeled as meanreverting OrnsteinUhlenbeck (OU) processes. The dynamic trading strategy is implemented as the solution to a stochastic optimal control problem that dynamically allocates capital over the spreads and a riskfree asset over a finite horizon to maximize a general constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA) utility function of the terminal wealth. We show that this stochastic control problem is computationally tractable. Specifically, we show that the coefficient functions defining the optimal feedback law are the solutions of a system of ordinary differential equations (ODEs) that are the essence of the tractability of the stochastic optimal control problem. We illustrate the dynamic trading strategy with four pairs that consist of seven S&P 500 index stocks, which shows that the performance achieved by the dynamic spread trading strategy is significant and robust to realistic transaction costs. Key words: convergence trading, dynamic trading, mean reversion, pairs trading, statistical arbitrage, stochastic optimal control. 1
ACC 2011 Tutorial Session: An Introduction to Option Trading from a Control Perspective
"... Abstract — The purpose of this tutorial session is to explain how controltheoretic tools and associated mathematical concepts can be used in option trading. No previous knowledge ..."
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Abstract — The purpose of this tutorial session is to explain how controltheoretic tools and associated mathematical concepts can be used in option trading. No previous knowledge
How Useful are MeanVariance Considerations in Stock Trading via Feedback Control?
"... Abstract — In classical finance, when a stochastic investment outcome is characterized in terms of its mean and variance, it is implicitly understood that the underlying probability distribution is not heavily skewed. For example, in the “perfect” case when outcomes are normally distributed, meanva ..."
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Abstract — In classical finance, when a stochastic investment outcome is characterized in terms of its mean and variance, it is implicitly understood that the underlying probability distribution is not heavily skewed. For example, in the “perfect” case when outcomes are normally distributed, meanvariance considerations tell the entire story. The main point of this paper is that meanvariance based measures of performance may be entirely inappropriate when a feedback control law is used instead of buyandhold to modulate one’s stock position as a function of time. For example, when using a feedback gain K to increment or decrement one’s stock position, we see that the resulting skewness measure S(K) for the trading gains or losses can easily become dangerously large. Hence, we argue in this paper that the selection of this gain K based on a classical meanvariance based utility function can lead to a distorted picture of the prospects for success. To this end, our analysis begins in a socalled idealized market with prices generated by Geometric Brownian Motion (GBM). In addition to the “red flag ” associated with skewness, a controller efficiency analysis is also brought to bear. While all feedback gains K lead to efficient (nondominated, Pareto optimal) controllers, in the meanvariance sense, we show that the same does not hold true when we use a returnrisk pair which incorporates more information about the probability distribution for gains and losses. To study the efficiency issue in an application context, the paper also includes a simulation for Pepsico Inc. using the last five years of historical data. I.
On the Linearity of Bayesian Interpolators for NonGaussian ContinuousTime AR(1) Processes
"... Abstract—Bayesian estimation problems involving Gaussian distributions often result in linear estimation techniques. Nevertheless, there are no general statements as to whether the linearity of the Bayesian estimator is restricted to the Gaussian case. The two common strategies for nonGaussian mode ..."
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Abstract—Bayesian estimation problems involving Gaussian distributions often result in linear estimation techniques. Nevertheless, there are no general statements as to whether the linearity of the Bayesian estimator is restricted to the Gaussian case. The two common strategies for nonGaussian models are either finding the best linear estimator or numerically evaluating the Bayesian estimator by Monte Carlo methods. In this paper, we focus on Bayesian interpolation of nonGaussian firstorder autoregressive (AR) processes where the driving innovation can admit any symmetric infinitely divisible distribution characterized by the Lévy–Khintchine representation theorem. We redefine the Bayesian estimation problem in the Fourier domain with the help of characteristic forms. By providing analytic expressions, we show that the optimal interpolator is linear for all symmetricstable distributions. The Bayesian interpolator can be expressed in a convolutive form where the kernel is described in terms of exponential splines. We also show that the limiting case of Lévytype AR(1) processes, the system of which has a pole at the origin, always corresponds to a linear Bayesian interpolator made of a piecewise linear spline, irrespective of the innovation distribution. Finally, we show the two mentioned cases to be the only ones within the family for which the Bayesian interpolator is linear. Index Terms—Alphastable innovation, autoregressive, Bayesian estimator, interpolation, Ornstein–Uhlenbeck process.