Results 1  10
of
14
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, ..."
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Cited by 17 (6 self)
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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...
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 ..."
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Cited by 6 (2 self)
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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
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 ..."
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Cited by 6 (0 self)
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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
Malliavin Calculus in Finance
, 2003
"... This article is an introduction to Malliavin Calculus for practitioners. ..."
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Cited by 5 (0 self)
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This article is an introduction to Malliavin Calculus for practitioners.
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 ..."
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Cited by 4 (1 self)
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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 ..."
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Cited by 3 (1 self)
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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.
The Benes Equation and Stochastic Calculus of Variations
 STOCHASTIC PROCESSES AND THEIR APPLICATIONS
, 1995
"... ..."
Elect. Comm. in Probab. 14 (2009), 457–463 ELECTRONIC COMMUNICATIONS in PROBABILITY A TYPE OF GAUSS ’ DIVERGENCE FORMULA ONWIENER SPACES
, 2009
"... spaces We will formulate a type of Gauss ’ divergence formula on sets of functions which are greater than a specific value of which boundaries are not regular. Such formula was first established by L. Zambotti in 2002 with a profound study of stochastic processes. In this paper we will give a much s ..."
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spaces We will formulate a type of Gauss ’ divergence formula on sets of functions which are greater than a specific value of which boundaries are not regular. Such formula was first established by L. Zambotti in 2002 with a profound study of stochastic processes. In this paper we will give a much shorter and simpler proof for his formula in a framework of the Malliavin calculus and give alternate expressions. Our approach also enables to show that such formulae hold in other Gaussian spaces. 1
Universit Ibn Tofal, Facult des Sciences
, 2003
"... This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter H 2 (0; 1) has an in¯nitely di®erentiable density on (0;1). The proof of this result is based on the techniques of the Malliavin calculus. 1 ..."
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This note is devoted to prove that the supremum of a fractional Brownian motion with Hurst parameter H 2 (0; 1) has an in¯nitely di®erentiable density on (0;1). The proof of this result is based on the techniques of the Malliavin calculus. 1