A consistency criterion for price impact functions in limit order markets is proposed that prohibits chain arbitrage exploitation. Both the bid-ask spread and the feedback of sequential market orders of the same kind onto both sides of the order book are essential to ensure consistency at the smallest time scale. All the stocks investigated in Paris Stock Exchange have consistent price impact f...

ABSTRKT The meaning of consistency of increased limit factors (ILF) is reconsidered and a new test of the consistency condition is proposed. It is shown that the three major measures of risk satisfy the new consistency test with no restrictions. The problems of specifying consistent risk-loaded rates for high limits are discussed and a revised subtraction formula is given for the case where ris...

In this lecture we return to the study of consistency properties of learning algorithms, where we will be interested in the question of whether the generalization error of the function learned by an algorithm approaches the Bayes error in the limit of infinite data. In particular, we will consider consistency properties of the simple k-nearest neighbor (k-NN) classification algorithm (in the ne...

Several consistency notions for lower previsions (coherence, convexity, others) require that the suprema of certain gambles, having the meaning of gains, are non-negative. The limit situation that a gain supremum is zero is termed Weak Dutch Book (WDB). In the literature, the special case of WDBs with precise probabilities has mostly been analysed, and strict coherence has been proposed as a ra...

We argue for the development of efficient methods to update the data plane state of an SDN, while maintaining desired consistency properties (e.g., no packet should be dropped). We highlight the inherent trade-off between the strength of the consistency property and dependencies it imposes among rules at different switches; these dependencies fundamentally limit how quickly data plane can be up...

We derive a set of consistency conditions for the pion-baryon coupling constants in the large-Nc limit of QCD. The consistency conditions have a unique solution which are precisely the values for the pion-baryon coupling constants in the Skyrme model. We also prove that non-relativistic SU(2Nf ) spin-flavor symmetry (where Nf is the number of light flavors) is a symmetry of the baryon-pion coup...

We propose a new class of mappings, called Dynamic Limit Growth Indices, that are designed to measure the long-run performance of a nancial portfolio in discrete time setup. We study various important properties for this new class of measures, and in particular, we provide necessary and su cient condition for a Dynamic Limit Growth Index to be a dynamic assessment index. We also establish their...

By superimposing a group structure on a sequence of projective probability spaces of Lebesgue measure preserving (l.m.p.) automorphisms of unit interval, the paper extends the Daniel-Kolmogorov consistency theorem that enables the construction of a measurable group structure with invariant Haar probability measure on an uncountably large projective limit space. The projective limit group is the...

We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+ ε dimensions as ε goes to zero, provided Newton’s constant scales with ε. Our procedure – spherical reduction, dualization, limit, dualizing back – passes several consistency tests: geometric properties, interactions with matter and the Bekenstein-Hawking entropy are as expected from Einstein gravity. Platinum Jub...

Developing distributed multiplayer games for ad-hoc networks is challenging. Consistency of the replicated shared state is hard to ensure at a low cost. Current consistency models and middleware systems lack the required adaptability and efficiency when applied to ad-hoc gaming. Hence, developing such robust applications is still a daunting task. We propose i) Vector-Field Consistency (VFC), a ...