Numerical algorithms for backward stochastic  differential equations with 1-d brownian motion:  Convergence and simulations***

Shige Peng; Mingyu Xu

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Numerical algorithms for backward stochastic differential equations with 1-d brownian motion: Convergence and simulations

Shige Peng, Mingyu Xu (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.

Bounds of Ruin Probabilities for Insurance Companies in the Presence of Stochastic Volatility on Investments

Mohamed Badaoui, Begoña Fernández (2011)

ESAIM: Proceedings

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In this work we consider a model of an insurance company where the insurer has to face a claims process which follows a Compound Poisson process with finite exponential moments. The insurer is allowed to invest in a bank account and in a risky asset described by Geometric Brownian motion with stochastic volatility that depends on an external factor modelled as a diffusion process. By using exponential martingale techniques we obtain upper...

Mucus dynamics subject to air and wall motion

S. Enault, D. Lombardi, P. Poncet, M. Thiriet (2010)

ESAIM: Proceedings

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This study presents a numerical investigation of basic interactions between respiratory mucus motion, air circulation and epithelium ciliated cells vibration. One focuses on identification of meaningful rheological parameters, physiological and numerical simulation dimensioning. These preliminary results are crucial before the study of more general configurations of respiratory mucus motion. The numerical study presented in this work...

A matrix-based numerical method for the simulation of the two-dimensional sine-Gordon equation,

Francisco de la Hoz (2012)

ESAIM: Proceedings

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This paper describes a numerical method for the two-dimensional sine-Gordon equation over a rectangular domain using differentiation matrices, in the theoretical frame of matrix differential equations.