Censored exploration and the dark pool problem

Ganchev, Kuzman; Nevmyvaka, Yuriy; Kearns, Michael; Vaughan, J.

doi:10.1145/1735223.1735247

Cited by 53 publications

(71 citation statements)

References 9 publications

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“…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%

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%

Market Making and Portfolio Liquidation Under Uncertainty

Nyström

Aly

Zhang

2014

Int. J. Theor. Appl. Finan.

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“…Ganchev et al. () and Laruelle et al. () establish learning algorithms to achieve optimal order split between dark pools.…”

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confidence: 99%

Portfolio Liquidation in Dark Pools in Continuous Time

Kratz

Schöneborn

2013

Mathematical Finance

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We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0, T ] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool. At the primary venue, trading yields a linear price impact. In the dark pool, no price impact costs arise but order execution is uncertain, modeled by a multi-dimensional Poisson process. We characterize the costs of trading by a linear-quadratic functional which incorporates both the price impact costs of trading at the primary exchange and the market risk of the position. The liquidation constraint implies a singularity of the value function of the resulting minimization problem at the terminal time T . Via the HJB equation and a quadratic ansatz, we obtain a candidate for the value function which is the limit of a sequence of solutions of initial value problems for a matrix differential equation. We show that this limit exists by using an appropriate matrix inequality and a comparison result for Riccati matrix equations. Additionally, we obtain upper and lower bounds of the solutions of the initial value problems, which allow us to prove a verification theorem. If a single asset position is to be liquidated, the investor slowly trades out of her position at the primary venue, with the remainder being placed in the dark pool at any point in time. For multi-asset liquidations this is generally not the case; it can, e.g., be optimal to oversize orders in the dark pool in order to turn a poorly balanced portfolio into a portfolio bearing less risk.

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“…One exception is by Ganchev et. al., but unfortunately their confidence bound depends on the scale and is not suitable for obtaining optimal regret bounds in our problem [10]. Another challenge is to improve the running time of the algorithms to O(1) per time step.…”

Section: Discussionmentioning

confidence: 98%

On Learning the Optimal Waiting Time

Lattimore

György

Szepesvári

2014

Lecture Notes in Computer Science

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Abstract. Consider the problem of learning how long to wait for a bus before walking, experimenting each day and assuming that the bus arrival times are independent and identically distributed random variables with an unknown distribution. Similar uncertain optimal stopping problems arise when devising power-saving strategies, e.g., learning the optimal disk spin-down time for mobile computers, or speeding up certain types of satisficing search procedures by switching from a potentially fast search method that is unreliable, to one that is reliable, but slower. Formally, the problem can be described as a repeated game. In each round of the game an agent is waiting for an event to occur. If the event occurs while the agent is waiting, the agent suffers a loss that is the sum of the event's "arrival time" and some fixed loss. If the agents decides to give up waiting before the event occurs, he suffers a loss that is the sum of the waiting time and some other fixed loss. It is assumed that the arrival times are independent random quantities with the same distribution, which is unknown, while the agent knows the loss associated with each outcome. Two versions of the game are considered. In the full information case the agent observes the arrival times regardless of its actions, while in the partial information case the arrival time is observed only if it does not exceed the waiting time. After some general structural observations about the problem, we present a number of algorithms for both cases that learn the optimal weighting time with nearly matching minimax upper and lower bounds on their regret.

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Censored exploration and the dark pool problem

Cited by 53 publications

References 9 publications

Market Making and Portfolio Liquidation Under Uncertainty

Market Making and Portfolio Liquidation Under Uncertainty

Portfolio Liquidation in Dark Pools in Continuous Time

On Learning the Optimal Waiting Time

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