Results 1 
9 of
9
Malliavin Calculus in Finance
, 2003
"... This article is an introduction to Malliavin Calculus for practitioners. ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
This article is an introduction to Malliavin Calculus for practitioners.
Computing the Distribution of the Maximum of a Gaussian Process
 IN AND OUT OF EQUILIBRIUM: PROBABILITY WITH A PHYSICAL FLAVOUR, PROGRESS IN PROBABILITY, BIRKHAUSER
, 2001
"... This paper deals with the problem of obtaining methods to compute the distribution of the maximum of a oneparameter stochastic process on a fixed interval, mainly in the Gaussian case. The main point is the relationship between the values of the maximum and crossings of the paths, via the socall ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
This paper deals with the problem of obtaining methods to compute the distribution of the maximum of a oneparameter stochastic process on a fixed interval, mainly in the Gaussian case. The main point is the relationship between the values of the maximum and crossings of the paths, via the socalled Rice's formulae for the factorial moments of crossings. In certain
Free Lunch and Arbitrage Possibilities in a Financial Market Model With an Insider
, 1999
"... We consider financial market models based on Wiener space with two agents on di#erent information levels: a regular agent whose information is contained in the natural filtration of the Wiener process W , and an insider who possesses some extra information from the beginning of the trading interval, ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We consider financial market models based on Wiener space with two agents on di#erent information levels: a regular agent whose information is contained in the natural filtration of the Wiener process W , and an insider who possesses some extra information from the beginning of the trading interval, given by a random variable L which contains information from the whole time interval. Our main concern are variables L describing the maximum of a pricing rule. Since for such L the conditional laws given the smaller knowledge of the regular trader up to fixed times are not absolutely continuous with respect to the law of L, this class of examples cannot be treated by means of the enlargement of filtration techniques as applied so far. We therefore use elements of a Malliavin and Ito calculus for measure valued random variables to give criteria for the preservation of the semimartingale property, the absolute continuity of the conditional laws of L with respect to its law, and the absence o...
Anticipating Stochastic Differential Equations of Stratonovich Type (Anticipating Stratonovich SDE)
, 1996
"... We prove existence and uniqueness for Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is g ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
We prove existence and uniqueness for Stratonovich stochastic differential equations where the coefficients and the initial condition may depend on the whole path of the driving Wiener process. Our main hypothesis is that the diffusion coefficient satisfies the Frobenius condition. The solution is given in terms of solutions of ordinary differential equations and the Wiener process. We use this representation to study properties of the solution.
MultiDimensional Fractional Brownian Motion And Some Applications To Queueing Theory
 In: Fractals in Engineering
, 1997
"... Superimposition of different traffic sources are modeled by a sum of fractional Brownian motions (with Hurst parameter varying in the whole range of (0; 1)) and a supplementary part which can be random. In this setting, it is shown that the overflow probability is non sensitive to this supplementary ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Superimposition of different traffic sources are modeled by a sum of fractional Brownian motions (with Hurst parameter varying in the whole range of (0; 1)) and a supplementary part which can be random. In this setting, it is shown that the overflow probability is non sensitive to this supplementary part. For the analysis of the fractional Brownian motions, new mathematical tools are provided.
Hitting times for Gaussian processes
 Ann. Probab
, 2008
"... We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and particular cases like the fractional Brownian motion are discussed. 1. Introduction. Consider ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We establish a general formula for the Laplace transform of the hitting times of a Gaussian process. Some consequences are derived, and particular cases like the fractional Brownian motion are discussed. 1. Introduction. Consider
The Benes Equation and Stochastic Calculus of Variations
 Stochastic Processes and Their Applications
, 1995
"... With the emergence of new technologies, new problems arise in the performance evaluation of queueing networks. Actually, it is believed that the Quality of Service of future networks will be determined mainly by the ability of switches to predict and hence control their input flow. The main model us ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
With the emergence of new technologies, new problems arise in the performance evaluation of queueing networks. Actually, it is believed that the Quality of Service of future networks will be determined mainly by the ability of switches to predict and hence control their input flow. The main model used to derive analytical properties of these systems is the G/D/1 queue with possibly finite buffers. In this setting, one often faces the problem of characterizing the input flow. This seems rather complicated because of the large amount of highly correlated and versatile sources. Several studies show that one can reasonably approximate the input streams with diffusion processes (possibly with jumps). This approximation works well in case of a large time scale, cf. Roberts (1991), or in case of superposition of several sources (see for instance RenKobayashi (1993)). In these fluid approximations, the buffer of the switch is modelized as a trunk w...
Chaotic extensions and the lent particle method for Brownian motion ∗
"... In previous works, we have developed a new Malliavin calculus on the Poisson space based on the lent particle formula. The aim of this work is to prove that, on the Wiener space for the standard OrnsteinUhlenbeck structure, we also have such a formula which permits to calculate easily and intuitive ..."
Abstract
 Add to MetaCart
In previous works, we have developed a new Malliavin calculus on the Poisson space based on the lent particle formula. The aim of this work is to prove that, on the Wiener space for the standard OrnsteinUhlenbeck structure, we also have such a formula which permits to calculate easily and intuitively the Malliavin derivative of a functional. Our approach uses chaos extensions associated to stationary processes of rotations of normal martingales.
The Lent Particle Method, Application to Multiple Poisson Integrals
, 2010
"... We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for the laws of random functionals of Lévy processes or solutions of stochastic differential equations with jumps. As in the Wiener ..."
Abstract
 Add to MetaCart
We give a extensive account of a recent new way of applying the Dirichlet form theory to random Poisson measures. The main application is to obtain existence of density for the laws of random functionals of Lévy processes or solutions of stochastic differential equations with jumps. As in the Wiener case the Dirichlet form approach weakens significantly the regularity assumptions. The main novelty is an explicit formula for the gradient or for the “carré du champ ” on the Poisson space called the lent particle formula because based on adding a new particle to the system, computing the derivative of the functional with respect to this new argument and taking back this particle before applying the Poisson measure. The article is expository in its first part and based on BouleauDenis [12] with several new examples, applications to multiple Poisson integrals are gathered in the last part which concerns the relation with the Fock space and some aspects of the second quantization.