General Intensity Shapes in Optimal Liquidation

Guéant, Olivier; Lehalle, Charles‐Albert

doi:10.1111/mafi.12052

Cited by 69 publications

(72 citation statements)

References 53 publications

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“…While a few papers attempt to consider the problem at the level of the interactions with the order book [2,53,55], most of them focus on the dynamics initiated by aggressive orders hitting a resilient order book and ignore trading with passive orders. In fact, optimal liquidation with limit orders included has only been studied very recently [10,19,32,34]. In this paper we consider trading algorithms which are at the most passive end of the spectrum and we focus on algorithms which use only passive limit orders placed in the limit order book.…”

Section: High Frequency Tradingmentioning

confidence: 99%

“…On the other hand, the presence of market risk favors faster trading. An optimal schedule of a large order may involve the use of market orders and limit orders in combination, as well as a routing of the orders to different exchanges including dark-pools [13,19,28,29,32,34,46,47]. During the continuous auction process implemented by most electronic trading pools, market participants send their orders to a queuing system where a first-in-first-out queue stands at each possible price.…”

Section: High Frequency Tradingmentioning

confidence: 99%

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Market Making and Portfolio Liquidation Under Uncertainty

Nyström

Aly

Zhang

2014

Int. J. Theor. Appl. Finan.

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Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.

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Section: High Frequency Tradingmentioning

confidence: 99%

Section: High Frequency Tradingmentioning

confidence: 99%

Market Making and Portfolio Liquidation Under Uncertainty

Nyström

Aly

Zhang

2014

Int. J. Theor. Appl. Finan.

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“…with the final condition: (15), (16), (7)- (9). Note that the right hand side of (64) is not a real valued function.…”

Section: The Optimal Trading Execution Strategy Of the Big Tradermentioning

confidence: 99%

“…The CARA function is the exponential of the final revenue minus the final cost of the trade. Finally in [9] Guéant introduces a model that can substitute Almgren's model [3]. In this model the trading execution strategy is a Poisson process whose intensity depends from the transactions volume.…”

Section: Introductionmentioning

confidence: 99%

A Trading Execution Model Based on Mean Field Games and Optimal Control

Fatone¹,

Mariani²,

Recchioni³

et al. 2014

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We present a trading execution model that describes the behaviour of a big trader and of a multitude of retail traders operating on the shares of a risky asset. The retail traders are modeled as a population of "conservative" investors that: 1) behave in a similar way, 2) try to avoid abrupt changes in their trading strategies, 3) want to limit the risk due to the fact of having open positions on the asset shares, 4) in the long run want to have a given position on the asset shares. The big trader wants to maximize the revenue resulting from the action of buying or selling a (large) block of asset shares in a given time interval. The behaviour of the retail traders and of the big trader is modeled using respectively a mean field game model and an optimal control problem. These models are coupled by the asset share price dynamic equation. The trading execution strategy adopted by the retail traders is obtained solving the mean field game model. This strategy is used to formulate the optimal control problem that determines the behaviour of the big trader. The previous mathematical models are solved using the dynamic programming principle. In some special cases explicit solutions of the previous models are found. An extensive numerical study of the trading execution model proposed is presented. The interested reader is referred to the website: http://www.econ.univpm.it/recchioni/finance/w19 to find material including animations, an interactive application and an app that helps the understanding of the paper. A general reference to the work of the authors and of their coauthors in mathematical finance is the website: http://www.econ.univpm.it/recchioni/finance. L. Fatone et al.3092

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“…In optimal execution problems, an agent is required to choose an efficient trading strategy for liquidating/acquiring a portfolio containing a large quantity of a given security in order to maximize her expected wealth (by minimizing cost or maximizing profit). In this problem formulation, there is a tradeoff between trading slowly to reduce market impact, or execution cost, and trading fast to reduce the risk of future uncertainty in prices (see e.g., Almgren and Chriss (2001); ; Gatheral et al (2012); Guéant and Lehalle (2013);Jaimungal and Kinzebulatov (2014); Cartea and Jaimungal (2016) among many others). Optimal limit order placement aims instead to benefit from buying low and selling high and benefit from the bid-ask spread without being adversely selected.…”

Section: Introductionmentioning

confidence: 99%

Mean-Field Games and Ambiguity Aversion

Huang

2017

SSRN Journal

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This thesis focuses on incorporating the idea of ambiguity aversion into mean-field games.Intuitively, mean-field games describes the dynamics of a system with an infinite population. It is useful in approximating systems with a large population, for which an exact result is computationally intractable. By adding in ambiguity aversion, the mean-field game reflects how players in the population should act if they wish to protect themselves from model misspecification.Two applications of mean-field games are considered through two distinct approaches.The broker execution problem is investigated in a multi-agent framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who search for statistical arbitrage strategies, and (iii) noise traders who buy and sell for exogenous reasons. All optimizing agents (the broker and HFTs) trade against noise traders as well as one another. We use a mean-field game approach to solve the problem and obtain a set of decentralized feedback trading strategies for the major and minor agents. Furthermore, the mean-field game strategies have an N -Nash equilibrium property where N → 0 as N → ∞.The second application focuses on interbank borrowing and lending, which may induce systemic risk into financial markets. A simple model of this is to assume that log-monetary reserves are coupled, and that banks can also borrow/lend from/to a central bank. When all banks optimize their cost of borrowing and lending, this leads to a stochastic game. We account for model uncertainty by recasting the problem as a robust stochastic game and succeed in providing a strategy which leads to a Nash equilibria for ii both the finite game and the mean-field game limit. We prove that an -Nash equilibrium exists and show that when firms are ambiguity-averse, default probabilities can be reduced relative to their ambiguity-neutral counterparts.Finally, this thesis develops a modified stochastic maximum principle for min-max problems, and derives new existence and uniqueness results for a mean-field game with ambiguity averse players. An -Nash equilibrium is shown to exist for this class of mean-field games, and the mean-field game equations are explicitly derived in the linearquadratic framework.iii

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General Intensity Shapes in Optimal Liquidation

Cited by 69 publications

References 53 publications

Market Making and Portfolio Liquidation Under Uncertainty

Market Making and Portfolio Liquidation Under Uncertainty

A Trading Execution Model Based on Mean Field Games and Optimal Control

Mean-Field Games and Ambiguity Aversion

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