Simultaneously long short trading in discrete and continuous time

Baumann, Michael Heinrich; Grüne, Lars

doi:10.1016/j.sysconle.2016.11.011

Cited by 12 publications

(7 citation statements)

References 8 publications

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“…Whereas robust portfolio balancing strategies have been presented in papers such as [4], the earliest contribution we find on robust positive expectation can be found in papers such as [5] and other related work by the same authors, such as [6]. In contrast to the above, we focus here on the linear feedback control framework which is covered in papers such as [1]- [3] and [7]- [12]. The body of literature motivating this paper includes a number of flavors for the underlying stock prices and the control structure.…”

Section: Introductionmentioning

confidence: 99%

“…The body of literature motivating this paper includes a number of flavors for the underlying stock prices and the control structure. For example, in reference [9], robustness results are given for stock prices generated by Merton's jump 1 Atul Deshpande is a graduate student working towards his doctoral dissertation in the Department of Electrical and Computer Engineering, University of Wisconsin, Madison, WI 53706. atul.deshpande@wisc.edu bob.barmish@wisc.edu diffusion model and references [10]- [12] address variants of the SLS controller for the discrete-time case. To conclude this brief survey, we note that most of the literature cited above falls within the robust control paradigm formulated in [13].…”

Section: Introductionmentioning

confidence: 99%

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A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control

Deshpande

Barmish

2018

2018 European Control Conference (ECC)

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The starting point of this paper is the so-called Robust Positive Expectation (RPE) Theorem, a result which appears in literature in the context of Simultaneous Long-Short stock trading. This theorem states that using a combination of two specially-constructed linear feedback trading controllers, one long and one short, the expected value of the resulting gain-loss function is guaranteed to be robustly positive with respect to a large class of stochastic processes for the stock price. The main result of this paper is a generalization of this theorem. Whereas previous work applies to a single stock, in this paper, we consider a pair of stocks. To this end, we make two assumptions on their expected returns. The first assumption involves price correlation between the two stocks and the second involves a bounded non-zero momentum condition. With known uncertainty bounds on the parameters associated with these assumptions, our new version of the RPE Theorem provides necessary and sufficient conditions on the positive feedback parameter K of the controller under which robust positive expectation is assured. We also demonstrate that our result generalizes the one existing for the single-stock case. Finally, it is noted that our results also can be interpreted in the context of pairs trading.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control

Deshpande

Barmish

2018

2018 European Control Conference (ECC)

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“…Using (10) with x = K L and x = −K S , respectively, gives ∂g/∂K L ≥ 0 and ∂g/∂K S ≥ 0. Therefore, the incremental gain, (9), is positive whenever dK L and dK S are positive, so that g(t) is increasing in K L and K S , and, hence, in K and β (since…”

Section: Positive Gain In Gslsmentioning

confidence: 99%

“…Further developments in this area included the consideration of interest rates and collateral requirements [5,6,15,7]. This work culminated in [8] which laid the foundations for many future research directions such as using a controller with delay [14], different price process models [10,9], time varying price evolution parameters [20] and also the use of a proportional-integral (PI) controller rather than the proportional controller which was used in the original SLS strategy [16].…”

Section: Introductionmentioning

confidence: 99%

A Generalized Framework for Simultaneous Long-Short Feedback Trading

O'Brien,

Burke,

Burke

2018

Preprint

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We present a generalization of the Simultaneous Long-Short (SLS) trading strategy described in recent control literature wherein we allow for different parameters across the short and long sides of the controller; we refer to this new strategy as Generalized SLS (GSLS). Furthermore, we investigate the conditions under which positive gain can be assured within the GSLS setup for both deterministic stock price evolution and geometric Brownian motion. In contrast to existing literature in this area (which places little emphasis on the practical application of SLS strategies), we suggest optimization procedures for selecting the control parameters based on historical data, and we extensively test these procedures across a large number of real stock price trajectories (495 in total). We find that the implementation of such optimization procedures greatly improves the performance compared with fixing control parameters, and, indeed, the GSLS strategy outperforms the simpler SLS strategy in general.

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“…For example, the SLS theory involves RPE results with respect to stock prices having time-varying drift and volatility; see [7], prices generated from Merton's diffusion model [8], generalization from a static linear feedback to the case of Proportional-Integral (PI) controllers [9], and discrete-time systems with delays [10]. More recently, in [11], an SLS control with cross-coupling is proposed to trade two stocks.…”

Section: Introductionmentioning

confidence: 99%

On Robust Optimal Linear Feedback Stock Trading

Hsieh¹

2022

Preprint

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The take-off point for this paper is the Simultaneous Long-Short (SLS) control class, which is known to guarantee the so-called robust positive expectation (RPE) property. That is, the expected cumulative trading gain-loss function is guaranteed to be positive for a broad class of stock price processes. This fact attracts many new extensions and ramifications to the SLS theory. However, it is arguable that a "systematic" way to select an optimal decision variable that is robust in the RPE sense is still unresolved. To this end, we propose a modified SLS control structure, which we call the double linear feedback control scheme, that allows us to solve the issue above for stock price processes involving independent returns. In this paper, we go beyond the existing literature by not only deriving explicit expressions for the expected value and variance of cumulative gain-loss function but also proving various theoretical results regarding robust positive expected growth and monotonicity. Subsequently, we propose a new robust optimal gain selection problem that seeks a solution maximizing the expected trading gain-loss subject to the prespecified standard deviation and RPE constraints. Under some mild conditions, we show that the optimal solution exists and is unique. Moreover, a simple graphical approach that allows one to systematically determine the optimal solution is also proposed. Finally, some numerical and empirical studies using historical price data are also provided to support our theory.

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Simultaneously long short trading in discrete and continuous time

Cited by 12 publications

References 8 publications

A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control

A Generalization of the Robust Positive Expectation Theorem for Stock Trading via Feedback Control

A Generalized Framework for Simultaneous Long-Short Feedback Trading

On Robust Optimal Linear Feedback Stock Trading

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