A diffusion approximation for limit order book models

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Horst, Ulrich¹  Kreher, Doerte¹ 

[1] Humboldt Univ, Berlin, Germany

关键词: Functional limit theorem;    Diffusion limit;    Scaling limit;    Convergence of stochastic differential equations;    Limit order book;   

DOI  :  10.1016/j.spa.2018.11.023

来源: Elsevier

【 摘 要 】

This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an R+-valued best bid price process and an L-loc(2)-valued volume process. It is shown that under suitable assumptions the sequence of interpolated discrete time models is relatively compact in a localized sense and that any limit point satisfies a certain infinite dimensional SDE. Under additional assumptions on the dependence structure we construct two classes of models, which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized sense. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free