Project Euclid

References

• [1] Avellaneda, M., Levy, A. and Parás, A. (1995). Pricing and hedging derivative securities in markets with uncertain volatilities. Appl. Math. Finance 2 73–88.
• [2] Bichteler, K. (1981). Stochastic integration and $L^{p}$-theory of semimartingales. Ann. Probab. 9 49–89.
  Mathematical Reviews (MathSciNet): MR606798
  Zentralblatt MATH: 0458.60057
  Digital Object Identifier: doi:10.1214/aop/1176994509
  Project Euclid: euclid.aop/1176994509
  
• [3] Cheridito, P., Soner, H. M., Touzi, N. and Victoir, N. (2007). Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs. Comm. Pure Appl. Math. 60 1081–1110.
  Mathematical Reviews (MathSciNet): MR2319056
  Zentralblatt MATH: 1121.60062
  Digital Object Identifier: doi:10.1002/cpa.20168
  
• [4] Denis, L., Hu, M. and Peng, S. (2011). Function spaces and capacity related to a sublinear expectation: Application to $G$-Brownian motion paths. Potential Anal. 34 139–161.
  Mathematical Reviews (MathSciNet): MR2754968
  Digital Object Identifier: doi:10.1007/s11118-010-9185-x
  
• [5] Denis, L. and Martini, C. (2006). A theoretical framework for the pricing of contingent claims in the presence of model uncertainty. Ann. Appl. Probab. 16 827–852.
  Mathematical Reviews (MathSciNet): MR2244434
  Zentralblatt MATH: 1142.91034
  Digital Object Identifier: doi:10.1214/105051606000000169
  Project Euclid: euclid.aoap/1151592252
  
• [6] Lyons, T. J. (1995). Uncertain volatility and the risk-free synthesis of derivatives. Appl. Math. Finance 2 117–133.
• [7] Mandelkern, M. (1990). On the uniform continuity of Tietze extensions. Arch. Math. (Basel) 55 387–388.
  Mathematical Reviews (MathSciNet): MR1076066
  Zentralblatt MATH: 0712.54009
  Digital Object Identifier: doi:10.1007/BF01198478
  
• [8] Nutz, M. and Soner, H. M. (2012). Superhedging and dynamic risk measures under volatility uncertainty. SIAM J. Control Optim. 50 2065–2089.
  Mathematical Reviews (MathSciNet): MR2974730
  Zentralblatt MATH: 1263.91026
  Digital Object Identifier: doi:10.1137/100814925
  
• [9] Pardoux, É. and Peng, S. G. (1990). Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 55–61.
  Mathematical Reviews (MathSciNet): MR1037747
  
• [10] Peng, S. (1997). Backward SDE and related $g$-expectation. In Backward Stochastic Differential Equations (Paris, 1995–1996). Pitman Research Notes in Mathematics Series 364 141–159. Longman, Harlow.
  Mathematical Reviews (MathSciNet): MR1752680
  Zentralblatt MATH: 0892.60066
  
• [11] Peng, S. (2004). Filtration consistent nonlinear expectations and evaluations of contingent claims. Acta Math. Appl. Sin. Engl. Ser. 20 191–214.
  Mathematical Reviews (MathSciNet): MR2064000
  Zentralblatt MATH: 1061.60063
  Digital Object Identifier: doi:10.1007/s10255-004-0161-3
  
• [12] Peng, S. (2005). Nonlinear expectations and nonlinear Markov chains. Chin. Ann. Math. Ser. B 26 159–184.
  Mathematical Reviews (MathSciNet): MR2143645
  Zentralblatt MATH: 1077.60045
  Digital Object Identifier: doi:10.1142/S0252959905000154
  
• [13] Peng, S. (2007). $G$-expectation, $G$-Brownian motion and related stochastic calculus of Itô type. In Stochastic Analysis and Applications. Abel Symp. 2 541–567. Springer, Berlin.
  Mathematical Reviews (MathSciNet): MR2397805
  Digital Object Identifier: doi:10.1007/978-3-540-70847-6_25
  
• [14] Peng, S. (2008). Multi-dimensional $G$-Brownian motion and related stochastic calculus under $G$-expectation. Stochastic Process. Appl. 118 2223–2253.
  Mathematical Reviews (MathSciNet): MR2474349
  Zentralblatt MATH: 1158.60023
  Digital Object Identifier: doi:10.1016/j.spa.2007.10.015
  
• [15] Peng, S. (2010). Nonlinear expectations and stochastic calculus under uncertainty. Preprint. Available at arXiv:1002.4546v1.
  arXiv: arXiv:1002.4546v1
  
• [16] Peng, S. (2010). Backward stochastic differential equation, nonlinear expectation and their applications. In Proceedings of the International Congress of Mathematicians. Volume I 393–432. Hindustan Book Agency, New Delhi.
  Mathematical Reviews (MathSciNet): MR2827899
  Zentralblatt MATH: 1233.60031
  
• [17] Soner, H. M., Touzi, N. and Zhang, J. (2013). Dual formulation of second order target problems. Ann. Appl. Probab. 23 308–347.
  Mathematical Reviews (MathSciNet): MR3059237
  Zentralblatt MATH: 06157190
  Digital Object Identifier: doi:10.1214/12-AAP844
  Project Euclid: euclid.aoap/1359124388
  
• [18] Soner, H. M., Touzi, N. and Zhang, J. (2012). Wellposedness of second order backward SDEs. Probab. Theory Related Fields 153 149–190.
  Mathematical Reviews (MathSciNet): MR2925572
  Zentralblatt MATH: 1252.60056
  Digital Object Identifier: doi:10.1007/s00440-011-0342-y
  
• [19] Stroock, D. W. and Varadhan, S. R. S. (1979). Multidimensional Diffusion Processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 233. Springer, Berlin.
  Mathematical Reviews (MathSciNet): MR532498