Second order approximations for limit order books

Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...

Second Order Approximations for Probability Models

In this paper, we derive a second order mean field theory for directed graphical probability models. By using an information theoretic argument it is shown how this can be done in the absense of a partition function. This method is the direct generalisation of the well-known TAP approximation for Boltzmann Machines. In a numerical example, it is shown that the method greatly improves the first ...

Stochastic Models for Service Systems and Limit Order Books

Time Consistent Dynamic Limit Order Books Calibrated on Options

In an incomplete nancial market, the axiomatic of Time Consistent Pricing Procedure (TCPP), recently introduced, is used to assign to any nancial asset a dynamic limit order book, taking into account both the dynamics of basic assets and the limit order books for options. Kreps-Yan fundamental theorem is extended to that context. A characterization of TCPP calibrated on options is given in term...

One-level limit order books with sparsity and memory

Motivated by Cont and Larrard (2013)’s seminal Limit Order Book (LOB) model, we propose two continuous-time models for the level I of a LOB in which the arrivals of limit orders, market orders, and cancellations are assumed to be mutually independent, memoryless, and stationary, but, unlike the aforementioned paper, the proposed models also account for some of the sparsity and memory exhibited ...