Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact

Neuman, Eyal; ss}, Moritz Vo{

doi:10.1137/20m1375486

Cited by 27 publications

(34 citation statements)

References 23 publications

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“…The results in this paper significantly improve the results of [37] as we allow for a general Volterra propagator instead of an exponential one. This turns the stochastic control problem to become non-Markovian as the state variables (e.g.…”

Section: Introductionsupporting

confidence: 67%

“…In this class of problems, sometimes temporary impact is also included, but trading signals are not taken into account, which leads to deterministic optimal strategies. In Neuman and Voß [37], the liquidation problem with an exponential propagator and a general semimartingale signal was solved and an explicit signal adaptive optimal strategy was derived.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Liquidation with Signals: the General Propagator Case

Jaber¹,

Neuman²

2022

Preprint

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We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as minimization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary L 2 -valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel.

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Section: Introductionsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Optimal Liquidation with Signals: the General Propagator Case

Jaber¹,

Neuman²

2022

Preprint

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“…As similarly show in Neuman and Voß (2022), a probabilistic and convex analytic calculus of variations approach can be readily applied to derive a system of coupled linear FBSDEs which characterises the unique solution to the minor agent's problem.…”

Section: Numerical Schemementioning

confidence: 99%

“…We show how the Stackelberg equilibrium can be found by backward induction, that is by first solving the minor agent's problem and then the major agent's problem. We determine the minor agent's optimal strategy via a calculus of variations argument, as similarly done in Neuman and Voß (2022). The following results also borrow ideas from Casgrain and Jaimungal (2019).…”

Section: Numerical Schemementioning

confidence: 99%

Fast and Slow Optimal Trading with Exogenous Information

Micheli¹,

Neuman²

2022

Preprint

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We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated orderflow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy.

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“…In other words, our model nests various existing proposals in the literature, offering a unified discrete-time framework that we investigate in detail. Other related work on optimal order execution with (exponentially) decaying (linear) transient price impact in discrete and continuous time include, e.g., Alfonsi et al [5], Alfonsi and Schied [8], Predoiu et al [49], Alfonsi et al [9], Gatheral et al [31], Lorenz and Schied [45], Alfonsi and Schied [7], Alfonsi and Acevedo [3], Bank and Fruth [17], Alfonsi and Blanc [4], Fruth et al [28,29], Graewe and Horst [33], Lehalle and Neuman [43], Horst and Xia [37], Chen et al [24], Ackermann et al [1,2], Forde et al [27], Neuman and Voß [46]. Moreover, in the linear case, we also establish a new explicit formula, see Proposition 1, for the optimal execution strategy with stochastic transient price impact and inventory penalty, which extends the explicit deterministic solution from Obizhaeva and Wang [47] and allows us to also accurately benchmark our machine learning approach.…”

Section: Introductionmentioning

confidence: 99%

On Parametric Optimal Execution and Machine Learning Surrogates

Chen¹,

Ludkovski²,

Voß³

2022

Preprint

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We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy, extending the deterministic results from Obizhaeva and Wang [47]. Second, we develop a numerical algorithm based on dynamic programming and deep learning for the case of nonlinear transient price impact as proposed by Bouchaud et al. [22]. Specifically, we utilize an actor-critic framework that constructs two neural-network (NN) surrogates for the value function and the feedback control. The flexible scalability of NN functional approximators enables parametric learning, i.e., incorporating several model or market parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the execution policy to these parameters. Our NN learner organically scales across multiple input dimensions and is shown to accurately approximate optimal strategies across a wide range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.

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Optimal Signal-Adaptive Trading with Temporary and Transient Price Impact

Cited by 27 publications

References 23 publications

Optimal Liquidation with Signals: the General Propagator Case

Optimal Liquidation with Signals: the General Propagator Case

Fast and Slow Optimal Trading with Exogenous Information

On Parametric Optimal Execution and Machine Learning Surrogates

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