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

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)

Citations:

Zbl 1259.60073
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