Diffusion approximation of recurrent schemes for financial markets, with application to the Ornstein-Uhlenbeck process
Abstract. We adapt the general conditions of the weak convergence for the sequence of processes with discrete time to the diffusion process towards the weak convergence for the discrete-time models of a financial market to the continuous-time diffusion model. These results generalize a classical scheme of the weak convergence for discrete-time markets to the Black-Scholes model. We give an explicit and direct method of approximation by a recurrent scheme. As an example, an Ornstein-Uhlenbeck process is considered as a limit model.
Keywords: diffusion approximation, semimartingale, recurrent scheme, financial market, multiplicative scheme, Ornstein-Uhlenbeck process.
Mathematics Subject Classification: 60F17, 60J60, 60G15, 91G80.