Hyperfinite construction of G-expectation

Tolulope Fadina, Frederik Herzberg

Research output: Contribution to journalArticlepeer-review


The hyperfinite G-expectation is a nonstandard discrete analogue of G-expectation (in the sense of Robinsonian nonstandard analysis). A lifting of a continuous-time G-expectation operator is defined as a hyperfinite G-expectation which is infinitely close, in the sense of nonstandard topology, to the continuous-time G-expectation. We develop the basic theory for hyperfinite G-expectations and prove an existence theorem for liftings of (continuous-time) G-expectation. For the proof of the lifting theorem, we use a new discretization theorem for the G-expectation (also established in this paper, based on the work of Dolinsky et al. [Weak approximation of G-expectations, Stoch. Process. Appl. 122(2) (2012), pp. 664–675]).

Original languageEnglish (US)
Pages (from-to)52-66
Number of pages15
Issue number1
StatePublished - Jan 2 2019
Externally publishedYes


  • G-expectation
  • hyperfinite discretization
  • lifting theorem
  • nonstandard analysis
  • volatility uncertainty
  • weak limit theorem

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation


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