Displaying similar documents to “Approximation of the Snell envelope and american options prices in dimension one”

Euler schemes and half-space approximation for the simulation of diffusion in a domain

Emmanuel Gobet (2001)

ESAIM: Probability and Statistics

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This paper is concerned with the problem of simulation of ( X t ) 0 ≤ t ≤ T , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain D : namely, we consider the case where the boundary ∂ D is killing, or where it is instantaneously reflecting in an oblique direction. Given N discretization times equally spaced on the interval [ 0 , T ] , we propose new discretization schemes: they are fully implementable and provide a weak error of order N - 1 under some conditions....

Probabilistic methods for semilinear partial differential equations. Applications to finance

Dan Crisan, Konstantinos Manolarakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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With the pioneering work of [Pardoux and Peng, (1990) 55–61; Pardoux and Peng, (1992) 200–217]. We have at our disposal stochastic processes which solve the so-called . These processes provide us with a Feynman-Kac representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear in many applications in the field of Mathematical Finance. Therefore there is a great interest among both practitioners and theoreticians...

Fast approximation of minimum multicast congestion – Implementation versus theory

Andreas Baltz, Anand Srivastav (2004)

RAIRO - Operations Research - Recherche Opérationnelle

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The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known N P -hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with m edges and k multicast requests, an r ( 1 + ε ) ( r t e x t O P T + exp ( 1 ) ln m ) -approximation can be computed in O ( k m ε - 2 ln k ln m ) time, where β bounds the time for computing an r -approximate minimum Steiner tree. Moreover, we present a new fast...

Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX

Bernard Roynette, Marc Yor (2010)

ESAIM: Probability and Statistics

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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 t - : = ∫ 0 t 1 X s < 0 d s , t ≥ 0 ) . On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion (see [B. Roynette, P. Vallois and M. Yor, (2006) 171–246]).

Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics

Mireille Bossy, Nicolas Champagnat, Sylvain Maire, Denis Talay (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of ℝ d . This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal...