A reduced basis for option pricing

We introduce a reduced basis method for the efficient numerical solution of partial integro-differential equations which arise in option pricing theory. Our method uses a basis of functions constructed from a sequence of Black-Scholes solutions with different volatilities. We show that this choice of basis leads to a sparse representation of option pricing functions, yielding an approximation whose precision is exponential in the number of basis functions. A Galerkin method using this basis for solving the pricing PDE is presented. Numerical tests based on the CEV diffusion model and the Merton jump diffusion model show that the method has better numerical performance relative to commonly used finite-difference and finite-element methods. We also compare our method with a numerical Proper Orthogonal Decomposition (POD). Finally, we show that this approach may be used advantageously for the calibration of local volatility functions.

Perfectly Matched Layers for the heat and advection-diffusion equations

We design a perfectly matched layer for the advection-diffusion equation. We show that the reflection coefficient is exponentially small with respect to the damping parameter and the width of the PML and this independently of the advection and of the viscosity. Numerical tests assess the efficiency of the approach

History of the solar flare radiation doses on-board aeroplanes using semi-empirical model and Concorde measurements

International audienc

History of the solar flare radiation doses on-board aeroplanes using semi-empirical model and Concorde measurements

International audienc

Radiation Doses Received by Commercial Aircrew

International audienc

Radiation Doses Received by Commercial Aircrew

International audienc

Semi-Empirical Model to Calculate Potential Radiation Exposure On Board Airplane During Solar Particle Events

International audienc

Radiation Doses Received by Commercial Aircrew

International audienc

Radiation Doses Received by Commercial Aircrew

International audienc

Radiation Doses Received by Commercial Aircrew

International audienc