Constructing sublinear expectations on path space

Stochastic Processes and their Applications

Volumn 123, Issue 8, 2013, Pages 3100-3121

  Nutz, Marcel ^a   Van Handel, Ramon ^b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b PRINCETON UNIVERSITY   (United States)

Author keywords

Analytic set; Dynamic programming; G expectation; Optional sampling; Random; Sublinear expectation; Time consistency

Indexed keywords

ANALYTIC SET; G-EXPECTATION; RANDOM; SUBLINEAR; TIME CONSISTENCY;

COMPUTER SIMULATION; DYNAMIC PROGRAMMING; STATISTICS; STOCHASTIC SYSTEMS;

SET THEORY;

EID: 84877842805     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spa.2013.03.022     Document Type: Article

References (26)

1. D.P. Bertsekas, and S.E. Shreve Stochastic Optimal Control. The Discrete-Time Case 1978 Academic Press New York
2. Lp-theory of semimartingales Ann. Probab. 9 1 1981 49 89
3. S. Cohen Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces Electron. J. Probab. 17 62 2012 1 15
4. D.L. Cohn Measure Theory 1980 Birkhäuser Boston
5. C. Dellacherie, and P.A. Meyer Probabilities and Potential A 1978 North Holland Amsterdam
6. C. Dellacherie, and P.A. Meyer Probabilities and Potential B 1982 North Holland Amsterdam
7. L. Denis, M. Hu, and S. Peng Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths Potential Anal. 34 2 2011 139 161
8. L. Denis, and C. Martini A theoretical framework for the pricing of contingent claims in the presence of model uncertainty Ann. Appl. Probab. 16 2 2006 827 852 (Pubitemid 44196534)
9. Y. Dolinsky, M. Nutz, and H.M. Soner Weak approximation of G-expectations Stochastic Process. Appl. 122 2 2012 664 675
10. H. Föllmer, and A. Schied Stochastic Finance: An Introduction in Discrete Time second ed. 2004 W. de Gruyter Berlin
11. V.G. Kanovei, and V.A. Lyubetskii On some classical problems of descriptive set theory Russian Math. Surveys 58 5 2003 839 927 (Pubitemid 38318014)
12. X. Li, and S. Peng Stopping times and related Itô's calculus with G-Brownian motion Stochastic Process. Appl. 121 7 2011 1492 1508
13. M. Nutz, Random G-expectations. Ann. Appl. Probab. (2010) (in press).
14. M. Nutz A quasi-sure approach to the control of non-Markovian stochastic differential equations Electron. J. Probab. 17 23 2012 1 23
15. M. Nutz, and H.M. Soner Superhedging and dynamic risk measures under volatility uncertainty SIAM J. Control Optim. 50 4 2012 2065 2089
16. S. Peng Filtration consistent nonlinear expectations and evaluations of contingent claims Acta Math. Appl. Sin. Engl. Ser. 20 2 2004 191 214 (Pubitemid 38932931)
17. S. Peng G-expectation, G-Brownian motion and related stochastic calculus of Itô type Stochastic Analysis and Applications Abel Symp. vol. 2 2007 Springer Berlin 541 567
18. S. Peng Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation Stochastic Process. Appl. 118 12 2008 2223 2253
19. S. Peng, Nonlinear expectations and stochastic calculus under uncertainty, 2010. Preprint. arXiv:1002.4546v1.
20. R.T. Rockafellar Integral functionals, normal integrands and measurable selections Nonlinear Operators and the Calculus of Variations Lecture Notes in Math. vol. 543 1976 Springer Berlin 157 207
21. H.M. Soner, N. Touzi, and J. Zhang Quasi-sure stochastic analysis through aggregation Electron. J. Probab. 16 2 2011 1844 1879
22. H.M. Soner, N. Touzi, and J. Zhang Wellposedness of second order backward SDEs Probab. Theory Related Fields 153 1-2 2012 149 190
23. H.M. Soner, N. Touzi, and J. Zhang Dual formulation of second order target problems Ann. Appl. Probab. 23 1 2013 308 347
24. Y. Song Properties of hitting times for G-martingales and their applications Stochastic Process. Appl. 121 8 2011 1770 1784
25. Y. Song Uniqueness of the representation for G-martingales with finite variation Electron. J. Probab. 17 24 2012 1 15
26. D. Stroock, and S.R.S. Varadhan Multidimensional Diffusion Processes 1979 Springer New York