Optimal trade execution under endogenous order flow

Chen, Ying; Horst, Ulrich; Tran, Hoang Hai

doi:10.2139/ssrn.3933364

Cited by 2 publications

(2 citation statements)

References 55 publications

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“…2 We require traders to be risk averse. The benchmark case of a deterministic risk-neutral single-player liquidation model can be solved in closed form as shown in Chen et al (2021). Even in this case, the impact kernel is different from the ones considered in the above mentioned papers.…”

Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

Portfolio liquidation games with self‐exciting order flow

Horst

Xia

2022

Mathematical Finance

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We analyze novel portfolio liquidation games with self-exciting order flow. Both the 𝑁-player game and the mean-field game (MFG) are considered. We assume that players' trading activities have an impact on the dynamics of future market order arrivals thereby generating an additional transient price impact. Given the strategies of her competitors each player solves a mean-field control problem. We characterize open-loop Nash equilibria in both games in terms of a novel mean-field FBSDE system with unknown terminal condition. Under a weak interaction condition, we prove that the FBSDE systems have unique solutions. Using a novel sufficient maximum principle that does not require convexity of the cost function we finally prove that the solution of the FBSDE systems do indeed provide open-loop Nash equilibria.

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Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

Portfolio liquidation games with self‐exciting order flow

Horst

Xia

2022

Mathematical Finance

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“…Single and multi-player liquidation models with self-exciting order flow and absolutely continuous controls where dZ t = ξ t dt have recently been considered in Chen et al [15] and Fu et al [23], respectively. In both models, the market order dynamics follows a Hawkes process with exponential kernel, and the large investor's trading triggers an additional flow of child orders whose rate increases linearly in the investor's traded volume.…”

Section: Introductionmentioning

confidence: 99%

A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies

Fu¹,

Horst²,

Xia³

2022

Preprint

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We consider a mean-field control problem with càdlàg semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and that it is of linear-quadratic form and that its coefficients satisfy a coupled system of non-standard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a sequence of discrete-time models. A sophisticated transformation shows that the system can be brought into standard Riccati form from which we deduce the existence of a global solution. Our analysis shows that the optimal strategy jumps only at the beginning and the end of the trading period.

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Optimal trade execution under endogenous order flow

Cited by 2 publications

References 55 publications

Portfolio liquidation games with self‐exciting order flow

Portfolio liquidation games with self‐exciting order flow

A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies

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