1,436,972 research outputs found
Dependent jump processes with coupled Lévy measures
No full textI present a simple method for the modeling and simulation of dependent positive jump processes through a series representation. Each constituent process is represented by a series whose terms are equal to a transformation of the jump times of a standard Poisson process. The transformations are given by the inverses of the respective marginal Lévy tail mass integral functions. The dependence between the various constituent processes is given by a probabilistic copula for the inter-arrival times of the various standard Poisson processes.Lévy copulas, Copulas, Lévy processes, Monte-Carlo simulations
Path dependent option pricing under Lévy processes applied to Bermudan options
No full textA model is developed that can price path dependent options when the underlying
process is an exponential Lévy process with closed form conditional characteristic
function. The model is an extension of a recent quadrature option pricing model so that it can be applied with the use of Fourier and Fast Fourier transforms.
Thus the model possesses nice features of both Fourier and quadrature option pricing techniques since it can be applied for a very general set of underlying Lévy processes and can handle exotic path dependent features. The model is applied to European and Bermudan options for geometric Brownian motion, a jump-diffusion process, a variance gamma process and a normal inverse Gaussian process. However it must be noted that the model can also price other path dependent exotic options such as lookback and Asian options
Some remarks on first passage of Lévy processes, the American put and pasting principles
No full textThe purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Lévy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195–220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663–1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process. Appl. 100 (2002) 75–107], Mordecki [Finance Stoch. 6 (2002) 473–493], Asmussen, Avram and Pistorius [Stochastic Process. Appl. 109 (2004) 79–111] and Chesney and Jeanblanc [Appl. Math. Fin. 11 (2004) 207–225] to the American perpetual put optimal stopping problem. Furthermore, we make folklore precise and give necessary and sufficient conditions for smooth pasting to occur in the considered problem
A Donsker Theorem for Lévy Measures
No full textGiven n equidistant realisations of a Lévy process (Lt; t >= 0), a natural estimator for the distribution function N of the Lévy measure is constructed. Under a polynomial decay restriction on the characteristic function, a Donsker-type theorem is proved, that is, a functional central limit theorem for the process in the space of bounded functions away from zero. The limit distribution is a generalised Brownian bridge process with bounded and continuous sample paths whose covariance structure depends on the Fourier-integral operator. The class of Lévy processes covered includes several relevant examples such as compound Poisson, Gamma and self-decomposable processes. Main ideas in the proof include establishing pseudo-locality of the Fourier-integral operator and recent techniques from smoothed empirical processes.uniform central limit theorem, nonlinear inverse problem, smoothed empirical processes, pseudo-differential operators, jump measure
Émile Benoit raconte ses souvenirs de jeunesse
No full textÉmile Benoit parle de divers sujets et raconte l'histoire de la région ainsi que son histoire personelle. Il parle de la vie quotidienne, du travail, des noms et du peuple de la région. -- Émile Benoit speaks on a variety of subjects and tells the history of the region as well as his personal history. He speaks of daily life, work, names, and the people of the region
Les archives Jean-Benoît Lévy ou le visible de l'archive
No full textInternational audienceEtude des archives du cinéaste Jean Benoit-Lévy
Διαδικασίες Lévy και θεωρία ρίσκου
No full textThis thesis is dedicated to the study of Lévy processes and their applications to Risk theory. A quick and accurate recount of some prerequisites and notions is provided at the start. Following that a comprehensive study regarding the Lévy processes follows. The first part ends with the showcasing of some representative Lévy processes. In the second part, the notions of Risk theory are presented and are linked to Lévy processes via a recount of the necessary theory. Everything comes together through the inclusion of some applications utilizing real world data. Additional toy examples and simulations are included, when appropriate, in the entirety of this thesis. The thesis concludes with a brief discussion focusing on the theory and material covered, as well as, personal opinions regarding avenues for future research on Lévy processes.Η παρούσα διατριβή είναι αφιερωμένη στη μελέτη των διαδικασιών Lévy και των εφαρμογών τους στη θεωρία ρίσκου. Στην αρχή γίνεται μια γρήγορη και ακριβής ανασκόπηση σε ορισμένες προαπαιτούμενες θεωρίες και έννοιες. Στη συνέχεια ακολουθεί μια ολοκληρωμένη μελέτη σχετικά με τις διαδικασίες Lévy. Το πρώτο μέρος ολοκληρώνεται με την παρουσίαση ορισμένων αντιπροσωπευτικών διαδικασιών Lévy. Στο δεύτερο μέρος παρουσιάζονται οι έννοιες της θεωρίας ρίσκου και συνδέονται με τις διαδικασίες Lévy μέσω μιας ανασκόπησης της απαραίτητης θεωρίας. Η τελική σύνδεση των περιεχομένων της διατριβής γίνεται μέσω της συμπερίληψης ορισμένων εφαρμογών που χρησιμοποιούν πραγματικά δεδομένα. Πρόσθετα παραδείγματα και προσομοιώσεις συμπεριλαμβάνονται, όταν χρειάζεται, στο σύνολο της παρούσας διατριβής. Η διατριβή ολοκληρώνεται με μια σύντομη συζήτηση που επικεντρώνεται στη θεωρία και το υλικό που καλύφθηκε, καθώς και με κάποιες προσωπικές απόψεις σχετικά με τις κατευθύνσεις για μελλοντική έρευνα σχετικά με τις διαδικασίες Lévy
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