Optimal Asset Liquidation with Multiplicative Transient Price Impact

Bilarev, Todor; Frentrup, Peter

doi:10.1007/s00245-017-9418-0

Cited by 17 publications

(16 citation statements)

References 38 publications

(62 reference statements)

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“…We now let µ : D × R → R and σ : D → R be two continuous maps such that, for all ε > 0, µ is Lipschitz, with linear growth in its second variable, on D ε,ε −1 × R, (4) σ is Lipschitz, with linear growth in its second variable, on D ε,ε −1 , where…”

Section: Abstract Market Impact Modelmentioning

confidence: 99%

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Second-Order Stochastic Target Problems with Generalized Market Impact

Bouchard

Loeper²,

Soner³

et al. 2019

SIAM J. Control Optim.

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We extend the study of [7,18] to stochastic target problems with general market impacts. Namely, we consider a general abstract model which can be associated to a fully nonlinear parabolic equation. Unlike [7,18], the equation is not concave and the regularization/verification approach of [7] can not be applied. We also relax the gamma constraint of [7]. In place, we need to generalize the a priori estimates of [18] and exhibit smooth solutions from the classical parabolic equations theory. Up to an additional approximating argument, this allows us to show that the super-hedging price solves the parabolic equation and that a perfect hedging strategy can be constructed when the coefficients are smooth enough. This representation leads to a general dual formulation. We finally provide an asymptotic expansion around a model without impact.

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Section: Abstract Market Impact Modelmentioning

confidence: 99%

“…To conclude, let us refer to [4,5,3,9,10,12,17,19,20,21], and the references therein. Also for related works, see [7] for a discussion.…”

Section: Introductionmentioning

confidence: 99%

Second-Order Stochastic Target Problems with Generalized Market Impact

Bouchard

Loeper²,

Soner³

et al. 2019

SIAM J. Control Optim.

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“…In order to represent price impact of renewables in power prices, which is more and more observed in several national power markets, we follow the common stream in literature (also in analogy with Koch and Vargiolu 2021) and represent renewable capacity installation as a nondecreasing process, thus resulting in a singular control problem. This is also analogous to other papers modeling price impact: for example, in problems of optimal execution, Becherer et al (2017) and Becherer et al (2018) take into account a multiplicative and transient price impact, whereas (Guo and Zervos 2015) consider an exponential parametrization in a geometric Brownian motion setting allowing for a permanent price impact. Also, a price impact model has been studied by Al Motairi and Zervos (2017), motivated by an irreversible capital accumulation problem with permanent price impact, and by Ferrari and Koch (2019), in which the authors consider an extraction problem with Ornstein-Uhlenbeck dynamics and transient price impact.…”

Section: Introductionmentioning

confidence: 74%

“…Also, a price impact model has been studied by Al Motairi and Zervos (2017), motivated by an irreversible capital accumulation problem with permanent price impact, and by Ferrari and Koch (2019), in which the authors consider an extraction problem with Ornstein-Uhlenbeck dynamics and transient price impact. In all of the aforementioned papers on price impact models dealing with singular stochastic controls (Al Motairi and Zervos 2017;Becherer et al 2017Becherer et al , 2018Ferrari and Koch 2019;Guo and Zervos 2015), the agents' actions can lead to an immediate jump in the underlying price process, whereas in our setting, it cannot. Our model is instead analogous to , , which show how to incorporate a market impact due to cross-border trading in electricity markets, and to Rowińska et al (2018), which models the price impact of wind electricity production on power prices.…”

Section: Introductionmentioning

confidence: 90%

Optimal installation of renewable electricity sources: the case of Italy

Awerkin

Vargiolu

2021

Decisions Econ Finan

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Starting from the model in Koch and Vargiolu (SIAM J Control Optim 59(4): 3068-3095, 2021), we test the real impact of current renewable installed power in the electricity price in Italy, and assess how much the renewable installation strategy which was put in place in Italy deviated from the optimal one obtained from the model in the period 2012-2018. To do so, we consider the Ornstein-Uhlenbeck (O-U) process, including an exogenous increasing process influencing the mean-reverting term, which is interpreted as the current renewable installed power. We estimate the parameters of this model by using real data of electricity prices and energy production from photovoltaic and wind power plants from the six main Italian price zones. We obtain that the model fits well the North, Central North and Sardinia zones: among these zones, the North is impacted by photovoltaic production, Sardinia by wind and the Central North does not present significant price impact. Then, we implement the solution of the singular optimal control problem of installing renewable power plants, in order to maximize the profit of selling the produced energy in the market net of installation costs. We extend the results of Koch and Vargiolu (SIAM J Control Optim 59(4): 3068-3095, 2021) to the case when no impact on power price is presented and to the case when N players can produce electricity by installing renewable power plants. To this extent, we analyze both the concepts of Pareto optima and of Nash equilibria. For this latter, we present a verification theorem in the 2-player case and an explicit characterization of a Nash equilibrium in the no-impact case. We are thus able to describe the optimal strategy and compare it with the real installation strategy that was put in place in Italy.

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“…Models in another subgroup extend the exponential decay of the price impact to general decay kernels, see Alfonsi et al [7], Gatheral et al [18]. Models with transient multiplicative price impact have recently been analyzed in Becherer et al [12,13], whereas Becherer et al [14] contains a stability result for the involved cost functionals. Superreplication and optimal investment in a block-shaped limit order book model with exponential resilience is discussed in Bank and Dolinsky [8,9] and in Bank and Voß [11].…”

Section: Introductionmentioning

confidence: 99%

Self-exciting price impact via negative resilience in stochastic order books

Ackermann¹,

Kruse²,

Urusov³

2021

Preprint

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Most of the existing literature on optimal trade execution in limit order book models assumes that resilience is positive. But negative resilience also has a natural interpretation, as it models self-exciting behaviour of the price impact, where trading activities of the large investor stimulate other market participants to trade in the same direction. In the paper we discuss several new qualitative effects on optimal trade execution that arise when we allow resilience to take negative values. We do this in a framework where both market depth and resilience are stochastic processes.

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Optimal Asset Liquidation with Multiplicative Transient Price Impact

Cited by 17 publications

References 38 publications

Second-Order Stochastic Target Problems with Generalized Market Impact

Second-Order Stochastic Target Problems with Generalized Market Impact

Optimal installation of renewable electricity sources: the case of Italy

Self-exciting price impact via negative resilience in stochastic order books

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