Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics) by Roger Mansuy

Cover of: Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics) | Roger Mansuy

Published by Springer .

Written in English

Read online

Subjects:

  • States of matter,
  • Science,
  • Filters (Mathematics),
  • Mathematics,
  • Science/Mathematics,
  • Probability & Statistics - General,
  • Brownian filtration,
  • Mathematics / Statistics,
  • Stopping times,
  • enlargement of filtration,
  • Chemistry - General,
  • Brownian motion processes,
  • Stochastic processes

Book details

The Physical Object
FormatPaperback
Number of Pages162
ID Numbers
Open LibraryOL9056012M
ISBN 103540294074
ISBN 109783540294078

Download Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics)

: Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics) (): Mansuy, Roger: BooksCited by: Random Times and Enlargements of Filtrations in a Brownian Setting. Authors: Mansuy, Roger, Yor, Marc attempts to characterize the Brownian filtration.

The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. Random Times and. Random Times and Enlargements of Filtrations in a Brownian Setting. Summary: the filtration of truncated Brownian motion; It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.

Download Citation | On Jan 1,Roger Mansuy and others published Random Times and Enlargement of Filtrations in a Brownian Setting | Find, read and cite. The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind.

It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of.

random times, enlargements of ltration and construction of market models. Historical background The rst part of this thesis is devoted to the study of enlargement of ltrations. Random times and enlargements of filtrations in a Brownian setting.

By R. Mansuy and M. Yor. Abstract. Coll. Lecture notes in mathematics n° Topics: [-PR] Mathematics [math]/Probability [] Publisher: Springer. Year: OAI identifier: oai:HAL:halv1. Random Times and Enlargements of Filtrations in a Brownian Setting. Series: Lecture Notes in Mathematics, Vol.Approx.

p., Softcover ISBN: Due: December 2, About this book In NovemberM. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. Mansuy R., Yor M. () Weak and Strong Brownian Filtrations.

In: Random Times and Enlargements of Filtrations in a Brownian Setting. Lecture Notes in Mathematics, vol Mansuy R., Yor M. () On the Martingales which Vanish on the Set of Brownian Zeroes.

In: Random Times and Enlargements of Filtrations in a Brownian Setting. Get this from a library. Random times and enlargements of filtrations in a Brownian setting. [Roger Mansuy; Marc Yor] -- In NovemberM. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York.

These notes follow the contents of that course, covering expansion of filtration formulae; BDG. Enlargements of filtrations --Stopping and non-stopping times --On the martingales which vanish on the set of Brownian zeroes --PRP and CRP Random Times and Enlargements of Filtrations in a Brownian Setting book some remarkable martingales --Unveiling the Brownian path (or history) as the level rises --Weak and strong Brownian filtrations --Sketches of solutions for.

Cite this chapter as: Mansuy R., Yor M. () Unveiling the Brownian Path (or history) as the Level Rises. In: Random Times and Enlargements of Filtrations in a Brownian Setting. Get this from a library. Random times and enlargements of filtrations in a Brownian setting. [Roger Mansuy; Marc Yor]. Progressive enlargements of filtrations with pseudo-honest times.

Ann. Appl. Probab. 24 – Mansuy, R. and Yor, M. Random Times and Enlargements of Filtrations in a Brownian Setting. Lecture Notes in Math. Springer, Berlin. Nikeghbali, A. and Yor, M. A definition and some characteristic properties of pseudo.

Enlargement of filtrations with random times for processes with jumps Article in Stochastic Processes and their Applications (7) July with 12 Reads How we measure 'reads'. Random Times and Enlargement of Filtrations in a Brownian Setting.

Article. Book. Jan ; Philip Protter Given a random time, we characterize the set of martingales for which the. Mansuy & M. Yor () Random Times and Enlargements of Filtrations in a Brownian Setting, Vol. Berlin: Springer. Google Scholar; A.

Mijatovic & M. Urusov () On the martingale property of certain local martingales, Probability Theory and Related Fields. Mansuy & M. Yor () Random Times and Enlargements of Filtrations in a Brownian Setting, Lecture Notes in Mathematics.

Berlin: Springer. Google Scholar; P. Schönbucher () Credit Derivatives Pricing Models: Models, Pricing and Implementation. New York: Wiley. Google Scholar. Mansuy and M. Yor, Random Times and Enlargements of Filtrations in a Brownian Setting, Lecture Notes in Mathematics (Springer, Berlin, ).

Google Scholar J. Mémin, Acta Mathematicae Applicatae Sinica, English Ser (). Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics Book ) by Roger Mansuy, Marc Yor. Mansuy R, Yor M () Random Times and Enlargements of Filtrations in a Brownian Setting, Berlin: Springer.

Merton RC () On the pricing of corporate debt: The risk structure of interest rates. J financ Mou L, Yong J () A variational formula for stochastic controls and some applications. Cite this chapter as: Mansuy R., Yor M.

() Sketches of Solutions for the Exercises. In: Random Times and Enlargements of Filtrations in a Brownian Setting. filtration is enlarged, and, in such a case, how to find the Doob-Meyer decomposition.

Filtrations may be enlarged in different ways. In this paper we consider initial and progressive filtration enlargements made by random variables and processes. Keywords: Credit Risk, Insider Trading, Enlargement of Filtrations. Marc Yor (24 July – 9 January ) was a French mathematician well known for his work on stochastic processes, especially properties of semimartingales, Brownian motion and other Lévy processes, the Bessel processes, and their applications to mathematical finance.

bounded FT-measurable) random variable. Stopping times A random variable ˝, valued in [0;1] is an F-stopping time if, for any t 0, f˝ tg 2 Ft.

A stopping time ˝is predictable if there exists an increasing sequence (˝n) of stopping times such that almost surely (i) limn˝n= ˝, (ii) ˝nset. Azéma associated with an honest time L the supermartingale and established some of its important properties. This supermartingale plays a central role in the general theory of stochastic processes and in particular in the theory of progressive enlargements of filtrations.

In this paper, we shall give an additive characterization for these supermartingales, which in turn will naturally provide. eBook Shop: Random Times and Enlargements of Filtrations in a Brownian Setting Lecture Notes in Mathematics von Roger Mansuy als Download.

Jetzt eBook. Random times and enlargements of filtrations in a brownian setting: Risques, options sur Hedge funds et produits hybrides: Selfdecomposable laws associated with hyperbolic functions: Semi-martingale Inequalities via the Garsia-Rodemich-Rumsey Lemma, and Applications to Local Times: Séminaire de probabilités: Some aspects of Brownian motion.

Discover Book Depository's huge selection of Roger Mansuy books online. Free delivery worldwide on over 20 million titles. () Let F t = σ(B s, 0 ≤ s ≤ t) denote the filtration generated by the Brownian motion B up to time instant t. Assume that G t is the enlargement of the filtration F t by knowing the random variables X 1, ÂÂÂ, X n at time t 1.

Enlargement of Filtration ([1] ) If G is a ltration larger than F, it is not true that an F-martingale is a G-martingale. K It o [3] was the rst to look at problems of enlargement of ltrations. From the seventies, Barlow, Jeulin and Yor started a systematic study of the problem of enlargement of ltrations.

Nikeghbali/The general theory of stochastic processes Definition The predictable σ-algebra P is the σ-algebra, defined on R+×Ω, generated by all processes (Xt)t≥0, adapted to (Ft), with left continuous paths on ]0,∞[.

This paper constructs a nonlinear filtering framework that admits appearances of new information processes at random times by introducing piecewise enlargements of filtrations and proposes a new energy-based Schrodinger evolution expressed as a stochastic differential equation on a complex Hilbert space.

Each information process is modeled as the sum of a random variable taking the eigenvalues. [50] R. M a n s u y, M. Y o r: Random times and (enlargement of filtrations) in a Brownian setting, Lecture Notes in Mathematics,Springer ().

MR [51] P.A. M e y e r: Processus de Markov, Lecture Notes in Mathemat Springer (). Request PDF | Initial Enlargement of Filtrations and Entropy of Poisson Compensators | Let μ be a Poisson random measure, let \mathbbF\mathbb{F} be the smallest filtration satisfying the usual.

London Math. Soc. 34 () –] gave an explicit example of a random time ρ associated with Brownian motion such that ρ is not a stopping time but E(Mρ)=E(M0) for every bounded martingale M. enlargement, where G = F _ ˙(L) where L is a random variable and the case of progressive enlargement where G is the smallest filtra-tion which contains F and makes a given positive random variable ˝ a stopping time.

The case where F is a Brownian filtration will be studied with more details. Applications to arbitrage opportunities in. ducing a new family of random times, as defined in [16] and called pseudo-stopping times, which generalize the fundamental notion of stopping times, introduced by J.L.

Doob. We take this opportunity to quote two passages, resp. in the appendix of Meyer’s book (): Les temps d’arrˆet ont ´et´e utilis´es, sans d´efinition formelle. In this note, using techniques of progressive enlargement of filtrations, we prove two theorems for the special, but important, cases when ρ is a pseudo-stopping time (Nikeghbali and Yor, ) or the end of a predictable set.

At an abstract level, this set-up can be considered an example of grossissement—the enlargement of filtrations. This theory was developed from the late s on, starting with the works of Barlow [6], Jeulin & Yor [25], [26], [27], and further developed by others including Yoeurp [35], and by Itô’s extension of the stochastic integral.Lecture Notes in Mathematics (共册), 这套丛书还有 《Topological Complexity of Smooth Random Functions》,《Random Times and Enlargements of Filtrations in a Brownian Setting (Lecture Notes in Mathematics)》,《Conference on Group Theory》,《Representation Theory II.

The most studied family of random times, after stopping times, are ends of optional sets, also named honest times (such the last zero of the standard Brownian motion before a fixed time). A very powerful, but not so well known, technique for studying such random times is that of the progressive expansions or enlargements of filtrations.

87984 views Saturday, November 7, 2020