This paper proposes a new analytical approximation scheme for the representation of the forward- backward stochastic differential equations (FBSDEs) of Ma and Zhang (2002). In particular, we obtain an error estimate for the scheme applying Malliavin calculus method for the forward SDEs combined...

The paper proposes a new deep learning-based algorithm for high-dimensional Bermudan option pricing. This is the first study for arbitrary order discretization scheme in the Bermudan option pricing or the dynamic programming problems. The price of Bermudan option is well approximated by...

The paper gives a novel path integral formula inspired by large deviation theory and Malliavin calculus. The proposed finite-dimensional approximation of integrals on path space will be a new higher-order weak approximation of multidimensional stochastic differential equations where the dominant...

This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR...