Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models

Ackermann, Julia; Kruse, Thomas; Urusov, Mikhail

doi:10.1007/s00780-021-00464-5

Cited by 13 publications

(23 citation statements)

References 31 publications

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“…These two cases can all be viewed as a kind of anti-symmetry. (7) reversely closed respect to a random parallel system (see Theorem 8); but (i) the inverse proposition of Theorem 8 does not hold. (ii) not reversely closed respect to a random series system.…”

Section: By Lemmas 3 and 4 We Know That Lnmentioning

confidence: 99%

“…When we need to compare the variability of two random variables, a good way to do this thing is by a partial order relation defined on a distribution class of random variables. In recent decades, many stochastic orders were defined early or late (see Shaked and Shanthikumar [1], Nanda and Paul [2,3], Kundu et al [4], Ghosh and Nanda [5], Gharari and Ganji [6], Ackermann et al [7], Sbert et al [8]). Of course, sometimes we need to infer the properties of individual (or a unit) from the properties of a population (or a system), then we say that this order has a closed property.…”

Section: Introductionmentioning

confidence: 99%

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On the Dynamic Cumulative Past Quantile Entropy Ordering

2021

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In many society and natural science fields, some stochastic orders have been established in the literature to compare the variability of two random variables. For a stochastic order, if an individual (or a unit) has some property, sometimes we need to infer that the population (or a system) also has the same property. Then, we say this order has closed property. Reversely, we say this order has reversed closure. This kind of symmetry or anti-symmetry is constructive to uncertainty management. In this paper, we obtain a quantile version of DCPE, termed as the dynamic cumulative past quantile entropy (DCPQE). On the basis of the DCPQE function, we introduce two new nonparametric classes of life distributions and a new stochastic order, the dynamic cumulative past quantile entropy (DCPQE) order. Some characterization results of the new order are investigated, some closure and reversed closure properties of the DCPQE order are obtained. As applications of one of the main results, we also deal with the preservation of the DCPQE order in several stochastic models.

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Section: By Lemmas 3 and 4 We Know That Lnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Dynamic Cumulative Past Quantile Entropy Ordering

2021

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“…Moreover, for each of these effects, we identify its reason by constructing pertinent examples. We also mention [1], which is a continuous-time counterpart of our present paper. In this connection it is worth noting that our results do not follow from the results in [1], but both papers rather concentrate on studying different questions: e.g., [1] does not study the qualitative effects mentioned in the previous paragraph (and discussed below); instead we need to work with a challenging quadratic BSDE in [1] and extend the continuous-time problem to incorporate execution strategies of infinite variation.…”

Section: Introductionmentioning

confidence: 99%

“…We also mention [1], which is a continuous-time counterpart of our present paper. In this connection it is worth noting that our results do not follow from the results in [1], but both papers rather concentrate on studying different questions: e.g., [1] does not study the qualitative effects mentioned in the previous paragraph (and discussed below); instead we need to work with a challenging quadratic BSDE in [1] and extend the continuous-time problem to incorporate execution strategies of infinite variation. In particular, some of the results of the present paper are required in [1] to derive, e.g., the appropriate problem formulation and the mentioned quadratic BSDE as continuous-time limits of the corresponding discrete-time objects.…”

Section: Introductionmentioning

confidence: 99%

“…The scientific literature on optimal trade execution problems deals with the optimization of trading schedules, when an investor faces the task of closing a position in an illiquid market. Incorporating random fluctuations of liquidity into models of optimal trade execution constitutes a highly active field of research (see, e.g., [1,6,7,8,9,11,12,14,16,17,18,19,20,22,24,26] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Optimal trade execution in an order book model with stochastic liquidity parameters

Ackermann¹,

Kruse²,

Urusov³

2020

Preprint

Self Cite

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We analyze an optimal trade execution problem in a financial market with stochastic liquidity. To this end we set up a limit order book model in which both order book depth and resilience evolve randomly in time. Trading is allowed in both directions and at discrete points in time. We derive an explicit recursion that, under certain structural assumptions, characterizes minimal execution costs. We also discuss several qualitative aspects of optimal strategies, such as existence of profitable round trips or closing the position in one go, and compare our findings with the literature.

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Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

Horst,

Kivman

2024

Finance Stoch

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We consider an optimal liquidation problem with instantaneous price impact and stochastic resilience for small instantaneous impact factors. Within our modelling framework, the optimal portfolio process converges to the solution of an optimal liquidation problem with general semimartingale controls when the instantaneous impact factor converges to zero. Our results provide a unified framework within which to embed the two most commonly used modelling frameworks in the liquidation literature and provide a foundation for the use of semimartingale liquidation strategies and the use of portfolio processes of unbounded variation. Our convergence results are based on novel convergence results for BSDEs with singular terminal conditions and novel representation results of BSDEs in terms of uniformly continuous functions of forward processes.

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Càdlàg semimartingale strategies for optimal trade execution in stochastic order book models

Cited by 13 publications

References 31 publications

On the Dynamic Cumulative Past Quantile Entropy Ordering

On the Dynamic Cumulative Past Quantile Entropy Ordering

Optimal trade execution in an order book model with stochastic liquidity parameters

Optimal trade execution under small market impact and portfolio liquidation with semimartingale strategies

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