We introduce the definition of a family of generating functions (FGF) of Toeplitz matrices, which is a generalization of the generating function of Toeplitz matrix. The FGF has an important application in pricing derivatives. The pricing of a European call option leads under certain assumptions...

We consider option pricing problems in the stochastic volatility jump diffusion model with correlated and contemporaneous jumps in both the return and the variance processes (SVCJ). The option value function solves a partial integro-differential equation (PIDE). We discretize this PIDE in space...

The value of a contingent claim under a jump-diffusion process satisfies a partial integro-differential equation (PIDE). We localize and discretize this PIDE in space by the central difference formula and in time by the second order backward differentiation formula. The resulting system Tnx = b...

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...

Constructing 2D/2D heterojunction photocatalysts has attracted the great attentions due to their inherent advantages. Herein, 2D/2D CoP/CdS heterojunctions were successfully fabricated and employed in photocatalytic H2 evolution using lactic acid as sacrificial reagents. The multiple...