Random $G$-expectations

Marcel Nutz

doi:10.1214/12-AAP885

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Home > Journals > Ann. Appl. Probab. > Volume 23 > Issue 5 > Article

October 2013 Random $G$-expectations

Marcel Nutz

Ann. Appl. Probab. 23(5): 1755-1777 (October 2013). DOI: 10.1214/12-AAP885

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Abstract

We construct a time-consistent sublinear expectation in the setting of volatility uncertainty. This mapping extends Peng’s $G$-expectation by allowing the range of the volatility uncertainty to be stochastic. Our construction is purely probabilistic and based on an optimal control formulation with path-dependent control sets.