Martingale representation theorem for the G-expectation

H. Mete Soner; Nizar Touzi; Jianfeng Zhang

doi:10.1016/j.spa.2010.10.006

Martingale representation theorem for the G-expectation

H. Mete Soner, Nizar Touzi, Jianfeng Zhang

Research output: Contribution to journal › Article › peer-review

144 Scopus citations

Abstract

This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16,17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target problems and the second-order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.

Original language	English (US)
Pages (from-to)	265-287
Number of pages	23
Journal	Stochastic Processes and their Applications
Volume	121
Issue number	2
DOIs	https://doi.org/10.1016/j.spa.2010.10.006
State	Published - Feb 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Modeling and Simulation
Applied Mathematics

Keywords

2BSDE
BSDE
G-expectation
G-martingale
duality
nonlinear expectation
singular measure
stochastic target problem

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10.1016/j.spa.2010.10.006

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abstract = "This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16,17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target problems and the second-order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.",

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AU - Touzi, Nizar

AU - Zhang, Jianfeng

PY - 2011/2

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N2 - This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16,17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target problems and the second-order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.

AB - This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16,17]. A martingale representation theorem for this theory is proved by using the techniques and the results established in Soner et al. (2009) [20] for the second-order stochastic target problems and the second-order backward stochastic differential equations. In particular, this representation provides a hedging strategy in a market with an uncertain volatility.

KW - 2BSDE

KW - BSDE

KW - G-expectation

KW - G-martingale

KW - duality

KW - nonlinear expectation

KW - singular measure

KW - stochastic target problem

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VL - 121

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EP - 287

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 2

ER -

Martingale representation theorem for the G-expectation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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