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Martingale representation theorem for the G-expectation

Author

Listed:
  • Soner, H. Mete
  • Touzi, Nizar
  • Zhang, Jianfeng

Abstract

This paper considers the nonlinear theory of G-martingales as introduced by Peng (2007) in [16] and [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.

Suggested Citation

  • Soner, H. Mete & Touzi, Nizar & Zhang, Jianfeng, 2011. "Martingale representation theorem for the G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 265-287, February.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:2:p:265-287
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    References listed on IDEAS

    as
    1. Xu, Jing & Zhang, Bo, 2009. "Martingale characterization of G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 232-248, January.
    2. Karandikar, Rajeeva L., 1995. "On pathwise stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 11-18, May.
    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
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