Publications

2005

• A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
  
  • Cont Rama
  • Voltchkova Ekaterina
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2005, 43 (4), pp.1596-1626. We present a finite difference method for solving parabolic partial integro-differential equations with possibly singular kernels which arise in option pricing theory when the random evolution of the underlying asset is driven by a Lévy process or, more generally, a time-inhomogeneous jump-diffusion process. We discuss localization to a finite domain and provide an estimate for the localization error under an integrability condition on the Lévy measure. We propose an explicit-implicit finite difference scheme which can be used to price European and barrier options in such models. We study stability and convergence of the scheme proposed and, under additional conditions, provide estimates on the rate of convergence. Numerical tests are performed with smooth and nonsmooth initial conditions. (10.1137/S0036142903436186)
  DOI : 10.1137/S0036142903436186
• Concentration for independent random variables with heavy tails
  
  • Barthe Franck
  • Cattiaux Patrick
  • Roberto Cyril
  AMRX Appl.Math.Res.Express, 2005 (2), pp.39-60. If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of $n$ independent copies, with good dependence in $n$.
• Generalized Impedance Impedance Boundary Conditions For Scattering by Strongly Absorbing Obstacles: The Scalar Case
  
  • Haddar Houssem
  • Joly Patrick
  • Nguyen Hoai-Minh
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2005, 15 (08), pp.1273-1300. (10.1142/S021820250500073X)
  DOI : 10.1142/S021820250500073X
• 3D piezoelectric surface green's function
  
  • Laude Vincent
  • Jerez-Hanckes Carlos F.
  • Ballandras Sylvain
  , 2005, pp.687-690.