Remarks on the transformation of Ito's formula for jump-diffusion processes

摘要

In this paper, we give detailed proofs of the transformation of the sum of the jump components that appears in Ito's formula for jump-diffusion processes into the stochastic integral with respect to a certain counting process. As applications of the transformed Ito's formula, the Black-Scholes equations in the compound Poisson process model and the jump-diffusion process model are discussed.