Call option prices based on Bessel processes (2008)
As a complement to some recent work by Pal and Protter, "Strict local martingales, bubbles, and no early exercise", we show that the call option prices associated with the Bessel strict local...
Penalising symmetric stable L\'evy paths (2008)
Yano, Kouji, Yano, Yuko, Yor, Marc
Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable L\'evy process of index $ 1 < \alpha \le 2 $. The first kind is a function...
These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first...
These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first...
These notes are the second half of the contents of the course given by the second author at the Bachelier Seminar (8-15-22 February 2008) at IHP. They also correspond to topics studied by the first...
A family of generalized gamma convoluted variables (2008)
Roynette, Bernard, Vallois, Pierre, Yor, Marc
This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that...
A family of generalized gamma convoluted variables (2008)
Roynette, Bernard, Vallois, Pierre, Yor, Marc
This paper consists of three parts: in the first part, we describe a family of generalized gamma convoluted (abbreviated as GGC) variables. In the second part, we use this description toprove that...
Renewal series and square-root boundaries for Bessel processes (2008)
Enriquez, Nathanael, Sabot, Christophe, Yor, Marc
We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...
Renewal series and square-root boundaries for Bessel processes (2008)
Enriquez, Nathanael, Sabot, Christophe, Yor, Marc
We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...
Renewal series and square-root boundaries for Bessel processes (2008)
Enriquez, Nathanael, Sabot, Christophe, Yor, Marc
We show how a description of Brownian exponential functionals as a renewal series gives access to the law of the hitting time of a square-root boundary by a Bessel process. This extends classical...
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first...
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first...
These notes are the first half of the contents of the course given by the second author at the Bachelier Seminar (February 8-15-22 2008) at IHP. They also correspond to topics studied by the first...
Madan, D., Roynette, Bernard, Yor, Marc
The authors recently discovered some interesting relations between the Black-Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous...
Madan, D., Roynette, Bernard, Yor, Marc
The authors recently discovered some interesting relations between the Black-Scholes formula and last passage times of the Brownian exponential martingales, which invites one to seek analogous...
We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before $t$, resp. first zero after $t$, of that Brownian motion. This study presents some analogy...
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the...
We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before $t$, resp. first zero after $t$, of that Brownian motion. This study presents some analogy...
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We develop a Brownian penalisation procedure related to weight processes $(F_t$) of the type : $F_t := f(I_t, S_t) where $f$ is a bounded function with compact support and $S_t (resp. I_t)$ is the...
From Black-Scholes formula, to local times and last passage times for certain submartingales (2008)
Madan, D., Roynette, Bernard, Yor, Marc
Motivated by an expression of the standard Black-Scholes formula as (a multiple of) the cumulative function of a certain distribution on $\/Bbb R_+$, we discuss a general extension of this identity...
From Black-Scholes formula, to local times and last passage times for certain submartingales (2008)
Madan, D., Roynette, Bernard, Yor, Marc
Motivated by an expression of the standard Black-Scholes formula as (a multiple of) the cumulative function of a certain distribution on $\/Bbb R_+$, we discuss a general extension of this identity...
Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX (2008)
We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional :...
A global view of Brownian penalisations (2008)
Najnudel, J., Roynette, Bernard, Yor, Marc
pas de résumé
Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX (2008)
We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional :...
A global view of Brownian penalisations (2008)
Najnudel, J., Roynette, Bernard, Yor, Marc
pas de résumé
On the time to reach maximum for a variety of constrained Brownian motions (2008)
Majumdar, Satya. N., Randon-Furling, Julien, Kearney, Michael J., Yor, Marc
We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit...
On the time to reach maximum for a variety of constrained Brownian motions (2008)
Majumdar, Satya. N., Randon-Furling, Julien, Kearney, Michael J., Yor, Marc
We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit...
Madan, D., Roynette, Bernard, Yor, Marc
The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving...
Madan, D., Roynette, Bernard, Yor, Marc
The celebrated Black-Scholes formula which gives the price of a European option, may be expressed as the cumulative function of a last passage time of Brownian motion. A related result involving...
On the time to reach maximum for a variety of constrained Brownian motions (2008)
Majumdar, Satya. N., Randon-Furling, Julien, Kearney, Michael J., Yor, Marc
We derive P(M,t_m), the joint probability density of the maximum M and the time t_m at which this maximum is achieved for a class of constrained Brownian motions. In particular, we provide explicit...
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new...
Generalized Gamma convolutions, Dirichlet means, Thorin measures with explicit examples (2007)
James, L.F., Roynette, Bernard, Yor, Marc
In section 1, we present a number of classical results concerning the generalized Gamma convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with Dirichlet processes. To a...
Generalized Gamma convolutions, Dirichlet means, Thorin measures with explicit examples (2007)
James, L.F., Roynette, Bernard, Yor, Marc
In section 1, we present a number of classical results concerning the generalized Gamma convolution ( : GGC) variables, their Wiener-Gamma representations, and relation with Dirichlet processes. To a...
Generalized Gamma Convolutions, Dirichlet means, Thorin measures, with explicit examples (2007)
James, Lancelot F., Roynette, Bernard, Yor, Marc
I. In Section 1, we present a number of classical results concerning the Generalized Gamma Convolution (: GGC) variables, their Wiener-Gamma representations, and relation with the Dirichlet...
We give a probabilistic interpretation for the Barnes G-function which appears in random matrix theory and in analytic number theory in the important moments conjecture due to Keating-Snaith for the...
Quasi-invariance properties of a class of subordinators (2007)
Von Renesse, Max-K., Yor, Marc, Zambotti, Lorenzo
We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of...
Quasi-invariance properties of a class of subordinators (2007)
Von Renesse, Max-K., Yor, Marc, Zambotti, Lorenzo
We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of...
Quasi-invariance properties of a class of subordinators (2007)
Von Renesse, Max-K., Yor, Marc, Zambotti, Lorenzo
We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of...
The characteristic polynomial of a random unitary matrix: a probabilistic approach (2007)
Bourgade, Paul, Hughes, Chris, Nikeghbali, Ashkan, Yor, Marc
In this paper, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix. We recover the Mellin Fourier transform of such a random polynomial, first...
Burkholder's submartingales from a stochastic calculus perspective (2007)
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...
Burkholder's submartingales from a stochastic calculus perspective (2007)
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...
Burkholder's submartingales from a stochastic calculus perspective (2007)
We provide a simple proof, as well as several generalizations, of a recent result by Davis and Suh, characterizing a class of continuous submartingales and supermartingales that can be expressed in...
Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2007)
Roynette, Bernard, Vallois, Pierre, Yor, Marc
Limiting laws for long Brownian Bridges perturbed by their one-sided maximum
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this...
Limiting laws for long Brownian Bridges perturbed by their one-sided maximum, III (2007)
Roynette, Bernard, Vallois, Pierre, Yor, Marc
Limiting laws for long Brownian Bridges perturbed by their one-sided maximum
On the excursion theory for linear diffusions (2007)
Salminen, Paavo, Vallois, Pierre, Yor, Marc
We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...
Penalizing a BES(d) process (0 < d < 2) with a function of its local time, V (2007)
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We study the penalization of a BES(d) process (0
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We give some extensions of Pitman's and Ray-Knight's theorems via a penalization procedure involving Brownian motion and its local time at 0
Donati-Martin, Catherine, Roynette, Bernard, Vallois, Pierre, Yor, Marc
We precise the choice of constants in computations related to Bessel processes with dimension d=2(1-alpha), 0 < alpha < 1
On the excursion theory for linear diffusions (2007)
Salminen, Paavo, Vallois, Pierre, Yor, Marc
We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...
Donati-Martin, Catherine, Roynette, Bernard, Vallois, Pierre, Yor, Marc
We precise the choice of constants in computations related to Bessel processes with dimension d=2(1-alpha), 0 < alpha < 1
Penalizing a BES(d) process (0 < d < 2) with a function of its local time, V (2007)
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We study the penalization of a BES(d) process (0
Roynette, Bernard, Vallois, Pierre, Yor, Marc
We give some extensions of Pitman's and Ray-Knight's theorems via a penalization procedure involving Brownian motion and its local time at 0
Euler's formulae for ζ(2n) and products of Cauchy variables (2007)
Bourgade, Paul; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Paulbourgade@gmail.com, Fujita, Takahiko; Graduate School Of Commerce And Management, Hitotsubashi University; Takahikofujita@mta.biglobe.ne.jp, Yor, Marc; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Deaproba@proba.jussieu.fr
We show how to recover Euler's formula for ζ(2n), as well as Lχ4(2n+1), for any integer n, from the knowledge of the density of the product of independent standard Cauchy variables.
Euler's formulae for ζ(2n) and products of Cauchy variables (2007)
Bourgade, Paul; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Paulbourgade@gmail.com, Fujita, Takahiko; Graduate School Of Commerce And Management, Hitotsubashi University; Takahikofujita@mta.biglobe.ne.jp, Yor, Marc; Laboratoire De Probabilités Et Modèles Aléatoires, Université Paris 6; Deaproba@proba.jussieu.fr
We show how to recover Euler's formula for ζ(2n), as well as Lχ4(2n+1), for any integer n, from the knowledge of the density of the product of independent standard Cauchy variables.
Two examples of functional penalisations of Brownian motion, VIII (2007)
On one hand, we penalise Brownian paths by a function of one-sided supremum of Brownian motion, considered up to the last, resp. the first, zero, before $t$, resp. after $t$. This study provides some...
Two examples of functional penalisations of Brownian motion, VIII (2007)
On one hand, we penalise Brownian paths by a function of one-sided supremum of Brownian motion, considered up to the last, resp. the first, zero, before $t$, resp. after $t$. This study provides some...
Euler's formula for zeta(2n) and Cauchy variables (2007)
Bourgade, Paul, Fujita, Takahiko, Yor, Marc
Euler's formulae for zeta(2n) are recovered from the computation in two dierent manners of the even moments of log(|C1C2|), for C1 and C2 two independent standard Cauchy variables. The method...
Euler's formula for zeta(2n) and Cauchy variables (2007)
Bourgade, Paul, Fujita, Takahiko, Yor, Marc
Euler's formulae for zeta(2n) are recovered from the computation in two dierent manners of the even moments of log(|C1C2|), for C1 and C2 two independent standard Cauchy variables. The method...
Tilted stable subordinators, Gamma time changes and Occupation Time of rays by Bessel Spiders (2007)
We exhibit, in the form of some identities in law, some connections between tilted stable subordinators, time-changed by independent Gamma processes and the occupation times of Bessel spiders, or...
On the excursion theory for linear diffusions (2006)
Salminen, Paavo, Vallois, Pierre, Yor, Marc
We present a number of important identities related to the excursion theory of linear diffusions. In particular, excursions straddling an independent exponential time are studied in detail. Letting...
Random Matrices and the Riemann zeta function (2006)
These notes are based on a talk given at the Institut de Mathématiques Elie Cartan de Nancy in June 2006. Their purpose is to introduce the reader to some links between two fields of mathematics :...
Random Matrices and the Riemann zeta function (2006)
These notes are based on a talk given at the Institut de Mathématiques Elie Cartan de Nancy in June 2006. Their purpose is to introduce the reader to some links between two fields of mathematics :...
Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc
The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...
Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc
The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...
Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc
The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...
Bertoin, J., Fujita, T., Roynette, Bernard, Yor, Marc
The distributional properties of the duration of a recurrent Bessel process straddling an independent exponential time are studied in detail. Althrough our study may be considered as a particular...
A chaotic representation property of the multidimensional Dunkl processes (2006)
Dunkl processes are martingales as well as c\`{a}dl\`{a}g homogeneous Markov processes taking values in $\mathbb{R}^d$ and they are naturally associated with a root system. In this paper we study the...
The laws of Brownian local time integrals (2006)
Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc
We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...
Abel transform and integrals of Bessel local times (2006)
Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc
We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...
The laws of Brownian local time integrals (2006)
Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc
We obtain some identities in law and some limit theorems for integrals of the type $\int_{0}^{t}\varphi(s)d{\rm L}_{s}$. Here $\varphi$ is a positive locally bounded Borel function and ${\rm L}_{t}$...
Abel transform and integrals of Bessel local times (2006)
Gradinaru, Mihai, Roynette, Bernard, Vallois, Pierre, Yor, Marc
We study integrals of the type $\int_{0}^{t}\varphi(s)dL_{s}$, where $\varphi$ is a positive locally bounded Borel function and $L_{t}$ denotes the local time at level 0 of a Bessel process of...
A chaotic representation property of the multidimensional Dunkl processes (2006)
Dunkl processes are martingales as well as càdlàg homogeneous Markov processes taking values in ℝd and they are naturally associated with a root system. In this paper we study the jumps of these...
Asymptotic laws for compositions derived from transformed subordinators (2006)
Gnedin, Alexander, Pitman, Jim, Yor, Marc
A random composition of n appears when the points of a random closed set ℛ̃⊂[0,1] are used to separate into blocks n points sampled from the uniform distribution. We study the number of parts Kn...
Options on Hedge Funds under the High Water Mark Rule (2006)
Atlan, Marc, Geman, Hélyette, Yor, Marc
The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...
Options on Hedge Funds under the High Water Mark Rule (2006)
Atlan, Marc, Geman, Hélyette, Yor, Marc
The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of...
We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...
We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...
We describe the CGMY and Meixner processes as time changed Brownian motions. The CGMY uses a time change absolutely continuous with respect to the one-sided stable $(Y/2)$ subordinator while the...