scholarly journals Effect of Cancel Order on Simple Stochastic Order-Book Model

2015 ◽  
pp. 75-84
Author(s):  
Shingo Ichiki ◽  
Katsuhiro Nishinari
Keyword(s):  
Stochastic Order ◽  
Order Book

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

2021 ◽  
Vol 25 (4) ◽  
pp. 757-810
Author(s):  
Julia Ackermann ◽  
Thomas Kruse ◽  
Mikhail Urusov
Keyword(s):  
Stochastic Order ◽  
Order Book ◽  
Optimal Trade Execution

A multilayer model of order book dynamics

2016 ◽  
Vol 2 (3) ◽  
pp. 37-52 ◽  
Author(s):  
Alessio Emanuele Biondo ◽  
Alessandro Pluchino ◽  
Andrea Rapisarda
Keyword(s):  
Order Book ◽  
Multilayer Model

Bid- and Ask-Side Liquidity in the NYSE Limit Order Book

2016 ◽  
Author(s):  
Tolga Cenesizoglu ◽  
Gunnar Grass
Keyword(s):  
Limit Order Book ◽  
Order Book ◽  
Limit Order

Predicting Liquidity from Order Book Data

2004 ◽  
Author(s):  
Knut Griese ◽  
Alexander Kempf
Keyword(s):  
Order Book

Volatility Regimes and the Provision of Liquidity in Order Book Markets

2004 ◽  
Author(s):  
Helena M. Beltran-Lopez ◽  
Alain C. J. Durré ◽  
Pierre Giot
Keyword(s):  
Order Book ◽  
Volatility Regimes ◽  
Book Markets

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

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