Shall I Sell or Shall I Wait? Optimal Liquidation Under Partial Information with Price Impact

Colaneri, Katia; Eksi, Zehra; Frey, Rüdiger; Szölgyenyi, Michaela

doi:10.2139/ssrn.2916154

Cited by 7 publications

(13 citation statements)

References 52 publications

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“…Others consider the possibility that their agents' models have the correct form; however, the agents must gradually learn the values of certain unobserved features ( [17], [31], [43], [54], [62], [48]). …”

Section: Background and Contributionsmentioning

confidence: 99%

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Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk

2017

SSRN Journal

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Abstract. Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision, fundamental value shocks, and market fragmentation. We develop a mathematical model which captures aspects of the first three explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they do, even just before their onset, market participants may not know with certainty that a disruption will unfold. Our mini-flash crashes can materialize in both low and high trading volume environments and may be accompanied by a partial synchronization in order submission.Instead of adopting a classically-inspired equilibrium approach, we borrow ideas from the optimal execution literature. Each of our agents begins with beliefs about how his own trades impact prices and how prices would move in his absence. They, along with other market participants, then submit orders which are executed at a common venue. Naturally, this leads us to explicitly distinguish between how prices actually evolve and our agents' opinions. In particular, every agent's beliefs will be expressly incorrect.As far as we know, this setup suggests both a new paradigm for modeling heterogeneous agent systems and a novel blueprint for understanding model misspecification risks in the context of optimal execution.

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Section: Background and Contributionsmentioning

confidence: 99%

“…A possible extension of our work could replace (4.2) with one of the more recent models considered in the literature on optimal trading problems with a learning aspect ( [17], [54], [43], [64], [86], [62], [48]). …”

Section: Preliminariesmentioning

confidence: 99%

Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk

2017

SSRN Journal

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“…In the upcoming part, we deal with the filtering problem corresponding to our setting by using the so called innovations approach. A similar problem is solved in [14] with a different methodology. In that paper, the dependence of the jump intensity of the stock price on the control lead to circularity of information which made it not possible to use the innovation approach.…”

Section: Optimization Problem Under Partial Informationmentioning

confidence: 99%

“…, and the value function of the optimization problem under partial information is (22) can be reduced to an optimization problem in an infinite horizon Markov decision model (MDM). Here we use the same techniques as in [14], to solve the utility maximization problem from terminal wealth. To give an idea, we show that the value function of the piecewise deterministic control problem can be identified as the value function of a certain Markov decision problem that can be solved by a fixed point argument, see [7,Chapter 8] for details.…”

Section: 2mentioning

confidence: 99%

“…To give an idea, we show that the value function of the piecewise deterministic control problem can be identified as the value function of a certain Markov decision problem that can be solved by a fixed point argument, see [7,Chapter 8] for details. Although the main technique used to handle the optimization problem is similar, we briefly explain the differences with [14]. In [14], the authors study an optimal liquidation problem for an investor whose actions directly affect the stock price dynamics by increasing the intensity of downward jumps in a partial information setting.…”

Section: 2mentioning

confidence: 99%

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Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

Altay¹,

Colaneri²,

Eksi³

2019

SIAM J. Finan. Math.

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We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility functions. In particular, we apply control theory for piecewise deterministic Markov processes (PDMP) to our problem and derive the optimality equation for the value function and characterize the value function as the unique viscosity solution of the associated dynamic programming equation. Finally, we provide a toy example, where the unobservable state process is driven by a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies as well as the optimal wealth under both partial and full information cases.

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Mini-Flash Crashes, Model Risk, and Optimal Execution

Bayraktar

Munk²

2018

Mark. Microstructure Liq.

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Oft-cited causes of mini-flash crashes include human errors, endogenous feedback loops, the nature of modern liquidity provision. We develop a mathematical model which captures aspects of these explanations. Empirical features of recent mini-flash crashes are present in our framework. For example, there are periods when no such events will occur. If they do, even just before their onset, market participants may not know with certainty that a disruption will unfold. Our miniflash crashes can materialize in both low and high trading volume environments and may be accompanied by a partial synchronization in order submission.Instead of adopting a classically-inspired equilibrium approach, we borrow ideas from the optimal execution literature. Each of our agents begins with beliefs about how his own trades impact prices and how prices would move in his absence. They, along with other market participants, then submit orders which are executed at a common venue. Naturally, this leads us to explicitly distinguish between how prices actually evolve and our agents' opinions. In particular, every agent's beliefs will be expressly incorrect.2010 Mathematics Subject Classification. Primary 91G80; Secondary 60H30, 60H10, 34M35.

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Shall I Sell or Shall I Wait? Optimal Liquidation Under Partial Information with Price Impact

Cited by 7 publications

References 52 publications

Mini-Flash Crashes, Model Risk, and Optimal Execution

Mini-Flash Crashes, Model Risk, and Optimal Execution

Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

Mini-Flash Crashes, Model Risk, and Optimal Execution

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