37 citations · 160 across the 20 of their papers we have counts for
22 papers
Representation and Integration by Parts Formulas for Affine Processes
Arturo Kohatsu-Higa, Yuma Tamura
Affine processes play an important role in mathematical finance and other applied areas due to their tractable structure. In the present article, we derive probabilistic representa…
Probabilistic representation of the gradient of a killed diffusion semigroup: The half-space case
Dan Crisan, Arturo Kohatsu-Higa
We introduce a probabilistic representation of the derivative of the semigroup associated to a multidimensional killed diffusion process defined on the half-space. The semigroup de…
A probabilistic representation of the derivative of a one dimensional killed diffusion semigroup
Dan Crisan, Arturo Kohatsu-Higa
We provide a probabilistic representation for the derivative of the semigroup corresponding to a diffusion process killed at the boundary of a half interval. In particular, we show…
Integration by parts formula for exit times of one dimensional diffusions
Noufel Frikha, Arturo Kohatsu-Higa, Libo Li
In line with the methodology introduced in our recent article for formulating probabilistic representations of integration by parts involving killed diffusion, we establish an inte…
Simulation of Reflected Brownian motion on two dimensional wedges
Pierre Bras, Arturo Kohatsu-Higa
We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide expl…
Density estimates for jump diffusion processes
Arturo Kohatsu-Higa, Eulalia Nualart, Ngoc Khue Tran
We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite mom…
Joint density of a stable process and its supremum: regularity and upper bounds
Jorge González Cázares, Arturo Kohatsu Higa, Aleksandar Mijatović
This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated s…
Asymptotic properties of the stochastic heat equation in large times
Arturo Kohatsu-Higa, David Nualart
In this article, we study the asymptotic behavior of the stochastic heat equation for large times.
Integration by parts formula for killed processes: A point of view from approximation theory
Noufel Frikha, Arturo Kohatsu-Higa, Libo Li
In this paper, we establish a probabilistic representation for two integration by parts formulas, one being of Bismut-Elworthy-Li's type, for the marginal law of a one-dimensional…
On the first hitting times of one dimensional elliptic diffusions
Noufel Frikha, Arturo Kohatsu-Higa, Libo Li
In this article, we obtain properties of the law associated to the first hitting time of a threshold by a one-dimensional uniformly elliptic diffusion process and to the associated…
A probabilistic interpretation of the parametrix method
Vlad Bally, Arturo Kohatsu-Higa
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a pro…
LAN property for an ergodic diffusion with jumps
Arturo Kohatsu-Higa, Eulalia Nualart, Ngoc Khue Tran
In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a pure-jump Lévy process with fi…
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…
LAN property for a linear model with jumps
Arturo Kohatsu-Higa, Eulalia Nualart, Ngoc Khue Tran
In this paper, we consider a linear model with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its intensity…
Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions
M. Besalú, A. Kohatsu-Higa, S. Tindel
In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parame…
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…
Local Hölder continuity property of the Densities of Solutions of SDEs with Singular Coefficients
Masafumi Hayashi, Arturo Kohatsu-Higa, Go Yuki
We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and Hölder continuous drift has a Hölder continuo…
Optimal simulation schemes for Lévy driven stochastic differential equations
Arturo Kohatsu-Higa, Salvador Ortiz-Latorre, Peter Tankov
We consider a general class of high order weak approximation schemes for stochastic differential equations driven by Lévy processes with infinite activity. These schemes combine a…
An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs
Hideyuki Tanaka, Arturo Kohatsu-Higa
Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler,…
A duality approach for the weak approximation of stochastic differential equations
Emmanuelle Clément, Arturo Kohatsu-Higa, Damien Lamberton
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation app…
Hints for an extension of the early exercise premium formula for American options
Hans-Peter Bermin, Arturo Kohatsu-Higa, Josep Perello
Characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numeric…
An application of Malliavin Calculus to Finance
Arturo Kohatsu-Higa, Miquel Montero
In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type opti…