AbstractWe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1009.2168.
Date of creation: Sep 2010
Date of revision: Sep 2013
Publication status: Published in Annals of Applied Probability 2013, Vol. 23, No. 5, 1755-1777
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-25 (All new papers)
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- Frederik Herzberg & Tolulope Fadina, 2014. "Weak approximation of G-expectation," Working Papers 503, Bielefeld University, Center for Mathematical Economics.
- Gordan Zitkovic, 2013. "Dynamic Programming for controlled Markov families: abstractly and over Martingale Measures," Papers 1307.5163, arXiv.org.
- Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
- Marcel Nutz & Ramon van Handel, 2012. "Constructing Sublinear Expectations on Path Space," Papers 1205.2415, arXiv.org, revised Apr 2013.
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