36 citations · 126 across the 37 of their papers we have counts for
24 papers · 1 filter
Ergodic approximation for the invariant distribution: An abstract framework for law-dependent dynamics
Aurélien Alfonsi, Vlad Bally, Lucia Caramellino +1
This paper studies the approximation of invariant distributions for a broad class of law-dependent dynamics, including McKean-Vlasov stochastic differential equations and Boltzmann…
Weak error approximation for rough and Gaussian mean-reverting stochastic volatility models
Aurélien Alfonsi, Ahmed Kebaier
For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using…
Euler-type approximation for the invariant measure: An abstract framework
Aurélien Alfonsi, Vlad Bally, Arturo Kohatsu-Higa
We establish a general framework to study the rate of convergence of a Euler type approximation scheme with decreasing time steps to the invariant measure, for a general class of s…
Wasserstein projections in the convex order: regularity and characterization in the quadratic Gaussian case
Aurélien Alfonsi, Benjamin Jourdain
In this paper, we first show continuity of both Wasserstein projections in the convex order when they are unique. We also check that, in arbitrary dimension , the quadratic Wass…
Quadratic Wasserstein distance between Gaussian laws revisited with correlation
Aurélien Alfonsi, Benjamin Jourdain
In this note, we give a simple derivation of the formula obtained in Dowson and Landau (1982), Olkin and Pukelsheim (1982) and Givens and Shortt (1984) for the quadratic Wasserstei…
Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
Eduardo Abi Jaber, Aurélien Alfonsi, Guillaume Szulda
We establish new weak existence results for -dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution…
On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients
Aurélien Alfonsi, Guillaume Szulda
We consider one-dimensional stochastic Volterra equations with jumps for which we establish conditions upon the convolution kernel and coefficients for the strong existence and pat…
Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation
Aurélien Alfonsi
This work defines and studies one-dimensional convolution kernels that preserve nonnegativity. When the past dynamics of a process is integrated with a convolution kernel like in S…
Construction of Boltzmann and McKean Vlasov type flows (the sewing lemma approach)
Aurélien Alfonsi, Vlad Bally
We are concerned with a mixture of Boltzmann and McKean-Vlasov type equations, this means (in probabilistic terms) equations with coefficients depending on the law of the solution…
Approximation of Stochastic Volterra Equations with kernels of completely monotone type
Aurélien Alfonsi, Ahmed Kebaier
In this work, we develop a multifactor approximation for -dimensional Stochastic Volterra Equations (SVE) with Lipschitz coefficients and kernels of completely monotone type tha…
A generic construction for high order approximation schemes of semigroups using random grids
Aurélien Alfonsi, Vlad Bally
Our aim is to construct high order approximation schemes for general semigroups of linear operators . In order to do it, we fix a time horizon and the discretiz…
Approximation of Optimal Transport problems with marginal moments constraints
Aurélien Alfonsi, Rafaël Coyaud, Virginie Ehrlacher +1
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of…
Squared quadratic Wasserstein distance : optimal couplings and Lions differentiability
Aurélien Alfonsi, Benjamin Jourdain
In this paper, we remark that any optimal coupling for the quadratic Wasserstein distance between two probability measures and with finite second order moments…
Sampling of probability measures in the convex order by Wasserstein projection
Aurélien Alfonsi, Jacopo Corbetta, Benjamin Jourdain
In this paper, for and two probability measures on with finite moments of order , we define the respective projections for the -Wasserstein dist…
Evolution of the Wasserstein distance between the marginals of two Markov processes
Aurélien Alfonsi, Jacopo Corbetta, Benjamin Jourdain
In this paper, we are interested in the time derivative of the Wasserstein distance between the marginals of two Markov processes. As recalled in the introduction, the Kantorovich…
Optimal transport bounds between the time-marginals of a multidimensional diffusion and its Euler scheme
Aurélien Alfonsi, Benjamin Jourdain, Arturo Kohatsu-Higa
In this paper, we prove that the time supremum of the Wasserstein distance between the time-marginals of a uniformly elliptic multidimensional diffusion with coefficients bounded t…
A remark on the optimal transport between two probability measures sharing the same copula
Aurélien Alfonsi, Benjamin Jourdain
We are interested in the Wasserstein distance between two probability measures on sharing the same copula . The image of the probability measure by the vectors of ps…
Stochastic Local Intensity Loss Models with Interacting Particle Systems
Aurélien Alfonsi, Céline Labart, Jérôme Lelong
It is well-known from the work of Schönbucher (2005) that the marginal laws of a loss process can be matched by a unit increasing time inhomogeneous Markov process, whose determini…
Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme
A. Alfonsi, B. Jourdain, A. Kohatsu-Higa
In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-di…
Strong convergence of some drift implicit Euler scheme. Application to the CIR process
Aurélien Alfonsi
We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi for the Cox-Ingersoll-Ross (CIR) process. Under general conditions, we o…
A Mean-Reverting SDE on Correlation matrices
Abdelkoddousse Ahdida, Aurélien Alfonsi
We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright-Fisher dif…
Exact and high order discretization schemes for Wishart processes and their affine extensions
Abdelkoddousse Ahdida, Aurélien Alfonsi
This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator…
General Duality for Perpetual American Options
Aurélien Alfonsi, Benjamin Jourdain
In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff is replaced by $…
A Call-Put Duality for Perpetual American Options
Aurélien Alfonsi, Benjamin Jourdain
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Cal…