A new algorithm, which is based on the splitting-step idea and the penalization method, for reflected stochastic differential equation (RSDE) in the upper half-space R¹<sub >+</sub> is presented in this paper. After some important estimates about RSDEs and penalization ODEs are obtained, the local pathwise...

In this paper, we develop a theta-discretization of time integrands for numerical solutions of forward-backward stochastic differential equations, and suggest a new set of basic functions to the Least -squares Monte Carlo simulations. This set of basic functions bases on characteristic functions...

We introduce a new class of basic functions based on characteristic functions to approximate two kinds of conditional expectations. we give the proofs and the error analysis of the approximations. In terms of such approximations, we employ a theta-discretization of time integrands for numerical...