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...

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...

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...