Numerical schemes for \(G\)-expectations. (English) Zbl 1283.60046

Dolinsky, Yan

Electron. J. Probab. 17, Paper No. 98, 15 p. (2012).

Summary: We consider a discrete time analog of \(G\)-expectations and prove that in the case where the time step goes to zero the corresponding values converge to the original \(G\)-expectation. Furthermore, we provide error estimates for the convergence rate. This paper is continuation of the one by Y. Dolinsky, M. Nutz and H. M. Soner [Stochastic Processes Appl. 122, No. 2, 664–675 (2012; Zbl 1259.60073)]. Our main tool is a strong approximation theorem which we derive for general discrete time martingales.

MSC:

60F15	Strong limit theorems
60G44	Martingales with continuous parameter
91B24	Microeconomic theory (price theory and economic markets)

Keywords:

\(G\)-expectations; volatility uncertainty; strong approximation theorems

Citations:

Zbl 1259.60073