Analytical approximations of BSDEs with non-smooth driver

Emmanuel Gobet (1) , Stefano Pagliarani (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We provide and analyse analytical approximations of BSDEs in the limit of small non-linearity {and short time}, in the case of non-smooth drivers. We identify the first and the second order approximations within this asymptotics and consider two topical financial applications: the two interest rates problem and the Funding Value Adjustment. In high dimensional diffusion setting, we show how to compute explicitly the first order formula by taking advantage of recent proxy techniques. Numerical tests up to dimension 10 illustrate the efficiency of the numerical schemes.

Mots clés: backward stochastic differential equation; asymptotic expansion

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Stefano Pagliarani. Analytical approximations of BSDEs with non-smooth driver. SIAM Journal on Financial Mathematics, 2015, 6 (1), pp.919-958. ⟨10.1137/14100021X⟩. ⟨hal-01003913⟩