TY  - JOUR
ID  - Mishura2015
LB  - Mishura2015
AU  - Mishura, Yuliya
TI  - Diffusion approximation of recurrent schemes for financial markets, with application to the Ornstein-Uhlenbeck process
ST  - Diffusion approximation of recurrent schemes for financial markets, with application to the Ornstein-Uhlenbeck process
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2015
VL  - 35
IS  - 1
SP  - 99
EP  - 116
DO  - http://dx.doi.org/10.7494/OpMath.2015.35.1.99
UR  - http://dx.doi.org/10.7494/OpMath.2015.35.1.99
AB  - 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.
KW  - diffusion approximation
KW  - semimartingale
KW  - recurrent scheme
KW  - financial market
KW  - multiplicative scheme
KW  - Ornstein-Uhlenbeck process
SN  - 1232-9274
ER  -