Diffusion approximation of recurrent schemes for financial markets, with application to the Ornstein-Uhlenbeck process. (English) Zbl 1332.60049
Summary: 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.
MSC:
| 60F17 | Functional limit theorems; invariance principles |
| 60F05 | Central limit and other weak theorems |
| 60J60 | Diffusion processes |
| 60G15 | Gaussian processes |
| 91G80 | Financial applications of other theories |
Keywords:
diffusion approximation; weak convergence; recurrent scheme; Ornstein-Uhlenbeck process; semimartingale; financial market; multiplicative schemeReferences:
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