The Annals of Applied Probability

Random $G$-expectations

Marcel Nutz

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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.

Article information

Source
Ann. Appl. Probab. Volume 23, Number 5 (2013), 1755-1777.

Dates
First available in Project Euclid: 28 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1377696297

Digital Object Identifier
doi:10.1214/12-AAP885

Mathematical Reviews number (MathSciNet)
MR3114916

Zentralblatt MATH identifier
1273.93178

Subjects
Primary: 93E20: Optimal stochastic control 91B30: Risk theory, insurance
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.)

Keywords
$G$-expectation volatility uncertainty stochastic domain risk measure time-consistency

Citation

Nutz, Marcel. Random $G$-expectations. Ann. Appl. Probab. 23 (2013), no. 5, 1755--1777. doi:10.1214/12-AAP885. https://projecteuclid.org/euclid.aoap/1377696297.


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