Pathwise construction of stochastic integrals

Electronic Communications in Probability

Volumn 17, Issue , 2012, Pages

  Nutz, Marcel ^a  

^a Columbia University ^*  (United States)

Author keywords

Aggregation; G expectation; Medial limit; Non dominated model; Pathwise stochastic integral; Second order BSDE

Indexed keywords

EID: 84863441807     PISSN: None     EISSN: 1083589X     Source Type: Journal    
DOI: 10.1214/ECP.v17-2099     Document Type: Article

References (17)

1. p-theory of semimartingales, Ann. Probab. 9 (1981), no. 1, 49-89. MR-0606798
2. L. Denis and C. Martini, A theoretical framework for the pricing of contingent claims in the presence of model uncertainty, Ann. Appl. Probab. 16 (2006), no. 2, 827-852. MR-2244434
3. H. Föllmer, Calcul d'Itô sans probabilités, Séminaire de Probabilités XV, Lecture Notes in Math., vol. 850, Springer, Berlin, 1981, pp. 143-150. MR-0622559
4. D. H. Fremlin, Measure theory, vol. 5, Torres Fremlin, Colchester, 2008.
5. J. Jacod and A. N. Shiryaev, Limit theorems for stochastic processes, 2nd ed., Springer, Berlin, 2003. MR-1943877
6. R. L. Karandikar, On pathwise stochastic integration, Stochastic Process. Appl. 57 (1995), no. 1, 11-18. MR-1327950
7. P. B. Larson, The filter dichotomy and medial limits, J. Math. Log. 9 (2009), no. 2, 159-165. MR-2679437
8. X. Li and S. Peng, Stopping times and related Itô's calculus with G-Brownian motion, Stochastic Process. Appl. 121 (2011), no. 7, 1492-1508. MR-2802462
9. P. A. Meyer, Limites médiales, d'après Mokobodzki, Séminaire de Probabilités VII (1971/72), Lecture Notes in Math., vol. 321, Springer, Berlin, 1973, pp. 198-204. MR-0404564
10. M. Nutz and H. M. Soner, Superhedging and dynamic risk measures under volatility uncertainty, to appear in SIAM J. Control Optim.
11. S. Peng, Nonlinear expectations and stochastic calculus under uncertainty, Preprint arXiv:1002.4546v1 (2010).
12. H. M. Soner, N. Touzi, and J. Zhang, Dual formulation of second order target problems, to appear in Ann. Appl. Probab.
13. H. M. Soner, N. Touzi, and J. Zhang, Wellposedness of second order backward SDEs, to appear in Probab. Theory Related Fields.
14. H. M. Soner, N. Touzi, and J. Zhang, Martingale representation theorem for the G-expectation, Stochastic Process. Appl. 121 (2011), no. 2, 265-287. MR-2746175
15. H. M. Soner, N. Touzi, and J. Zhang, Quasi-sure stochastic analysis through aggregation, Electron. J. Probab. 16 (2011), no. 2, 1844-1879. MR-2842089
16. W. Willinger and M. S. Taqqu, Pathwise approximations of processes based on the fine structure of their filtration, Séminaire de Probabilités XXII, Lecture Notes in Math., vol. 1321, Springer, Berlin, 1988, pp. 542-599. MR-0960547
17. W. Willinger and M. S. Taqqu Pathwise stochastic integration and applications to the theory of continuous trading, Stochastic Process. Appl. 32 (1989), no. 2, 253-280. MR-1014453