We develop theory and applications of forward characteristic processes in discrete time following a seminal paper of Jan Kallsen and Paul Kr\"uhner. Particular emphasis is placed on the dynamics of volatility surfaces which can be easily formulated and implemented from the chosen discrete point...

We follow the main stocks belonging to the New York Stock Exchange and to Nasdaq from 2003 to 2012, through years of normality and of crisis, and study the dynamics of networks built on two measures expressing relations between those stocks: correlation, which is symmetric and measures how...

In this study we prove the existence of statistical arbitrage opportunities in the Black-Scholes framework by considering trading strategies that consists of borrowing from the risk free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive...

Toehold purchase, defined here as purchase of one share in a firm by an investor preparing a tender offer to acquire majority of shares in it, reduces by one the number of shares this investor needs for majority. In the paper we construct mathematical models for the toehold and no-toehold...

In this paper we consider the optimal transport approach for computing the model-free prices of a given path-dependent contingent claim in a two periods model. More precisely, we first specialize the optimal transport plan introduced in \cite{BeiglJuil}, following the construction of...

In order to study the geometry of interest rates market dynamics, Malliavin, Mancino and Recchioni [A non-parametric calibration of the HJM geometry: an application of It\^o calculus to financial statistics, {\it Japanese Journal of Mathematics}, 2, pp.55--77, 2007] introduced a scheme, which is...

A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the...

This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of high-frequency asset returns both in ordinary clock time and in...

The argument that the alarming level of Gini coefficient is 0.4 is very popular, especially in the media industry, all around the world for a long time. Although the 0.4 standard is widely accepted, the derivation of the value lacks rigid theoretical foundations. In fact, to the best of our...

We consider an arbitrage-free, discrete time and frictionless market. We prove that an investor maximising the expected utility of her terminal wealth can always find an optimal investment strategy provided that her dissatisfaction of infinite losses is infinite and her utility function is...