Abstract We explicitly quantize the Witt algebra in characteristic 0 equipped with its Lie bialgebra structures discovered by Taft. Then, we study the reduction modulo p of our formulas. This gives p… Expand

We correct the double spend race analysis given in Nakamoto's foundational Bitcoin article and give a closed-form formula for the probability of success of a double spend attack using the Regularized Incomplete Beta Function.Expand

We review the so called selfish mining strategy in the Bitcoin network and compare its profitability to honest mining even after a difficulty adjustment.Expand

We study selfish mining in Ethereum. The problem is combinato-rially more complex than in Bitcoin because of major differences in the reward system and a different difficulty adjustment formula.… Expand

The following text is a short version of a forthcoming preprint about torsors. The adopted viewpoint is an old reformulation of torsors recalled recently by Kontsevich [Kon]. We propose a unification… Expand

Abstract This article is made up with two parts. In the first part, using a recent result of Schauenburg, one generalizes to the case when objects are faithfully flat over the ground ring, the full… Expand

Nakamoto double spend strategy, described in Bitcoin foundational article, leads to total ruin with positive probability and does not make sense from the profitability point of view.Expand

We invert the Black-Scholes formula. We consider the cases low strike, large strike, short maturity and large maturity. We give explicitly the first 5 terms of the expansions. A method to compute all… Expand

The aim of this paper is to provide a new straightforward measure-free methodology based on convex hulls to determine the no-arbitrage pricing bounds of an option (European or American).Expand