arXiv subjects

José Manuel Corcuera

Publications and source records attributed to José Manuel Corcuera.

7 recordsLinked to original sources

arXiv2025

Fractional signature: a generalisation of the signature inspired by fractional calculus

In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the signature, inspired by the previous one, but more convenient to use in machine learning. Finally, we test this last signature in a toy application to the problem of handwritten digit recognition, where significant improvements in accuracy rates are observed compared to those of the original signature.

stat.ML↗

arXiv2021

The Golden Age of the Mathematical Finance

This paper is devoted to show that the last quarter of the past century can be considered as the golden age of the Mathematical Finance. In this period the collaboration of great economists and the best generation of probabilists, most of them from the Strasbourg's School led by Paul André Meyer, gave rise to the foundations of this discipline. They established the two fundamentals theorems of arbitrage theory, close formulas for options, the main modelling a

q-fin.MF↗

arXiv2018

A continuous auction model with insiders and random time of information release

In a unified framework we study equilibrium in the presence of an insider having information on the signal of the firm value, which is naturally connected to the fundamental price of the firm related asset. The fundamental value itself is announced at a future random (stopping) time. We consider two cases. First when the release time of information is known to the insider and then when it is unknown also to her. Allowing for very general dynamics, we study the structure of the insider's optimal strategies in equilibrium and we discuss market efficiency. In particular, we show that in the case the insider knows the information release time, the market is fully efficient. In the case the insider does not know this random time, we see that there is an equilibrium with no full efficiency, but where the sensitivity of prices is decreasing in time according with the probability that the announcement time is greater than the current time. In other words, the prices become more and more stable as the announcement approaches.

q-fin.PR↗

arXiv2016

CoCos under short-term uncertainty

In this paper we analyze an extension of the Jeanblanc and Valchev (2005) model by considering a short-term uncertainty model with two noises. It is a combination of the ideas of Duffie and Lando (2001) and Jeanblanc and Valchev (2005): share quotations of the firm are available at the financial market, and these can be seen as noisy information about the fundamental value, or the firm's asset, from which a low level produces the credit event. We assume there are also reports of the firm, release times, where this short-term uncertainty disappears. This credit event model is used to describe conversion and default in a CoCo bond.

q-fin.MF↗

arXiv2014

Asymptotics of weighted random sums

In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We show that these sums converge in law to the integral of the weight process with respect to the Brownian motion when the distance between observations goes to zero. The result is obtained with the help of fractional calculus showing the power of this technique. This study, though interesting by itself, is motivated by an error found in the proof of Theorem 4 in Corcuera, J.M. Nualart, D., Woerner, J. H. C. (2006). Power variation of some integral fractional processes, Bernoulli 12(4) 713-735.

math.PR↗

arXiv2012

Asymptotic theory for Brownian semi-stationary processes with application to turbulence

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in [Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2011): Multipower variation for Brownian semistationary processes. Bernoulli 17(4), 1159-1194; Barndorff-Nielsen, O.E., J.M. Corcuera and M. Podolskij (2012): Limit theorems for functionals of higher order differences of Brownian semi-stationary processes. In "Prokhorov and Contemporary Probability Theory", Springer.] and present some new connections to fractional diffusion models. We apply our probabilistic results to construct a family of estimators for the smoothness parameter of the BSS process. In this context we develop estimates with gaps, which allow to obtain a valid central limit theorem for the critical region. Finally, we apply our statistical theory to turbulence data.

math.PR↗

arXiv2012

Multipower variation for Brownian semistationary processes

In this paper we study the asymptotic behaviour of power and multipower variations of processes $Y$:\[Y_t=\int_{-\in fty}^tg(t-s)σ_sW(\mathrm{d}s)+Z_t,\] where $g:(0,\infty)\rightarrow\mathbb{R}$ is deterministic, $σ>0$ is a random process, $W$ is the stochastic Wiener measure and $Z$ is a stochastic process in the nature of a drift term. Processes of this type serve, in particular, to model data of velocity increments of a fluid in a turbulence regime with spot intermittency $σ$. The purpose of this paper is to determine the probabilistic limit behaviour of the (multi)power variations of $Y$ as a basis for studying properties of the intermittency process $σ$. Notably the processes $Y$ are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results, a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to the realised variance ratio are given.

math.ST↗