On quadratic g-evaluations/expectations and related analysis

Stochastic Analysis and Applications

Volumn 28, Issue 4, 2010, Pages 711-734

  Ma, Jin ^a,b   Yao, Song ^c  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^c UNIVERSITY OF MICHIGAN   (United States)

Author keywords

BMO; Doob Meyer decomposition; Jensen's inequality; Optional sampling; Quadratic g evaluations; Quadratic g expectations; Reverse comparison theorem; Upcrossing inequality

Indexed keywords

EID: 77953320884     PISSN: 07362994     EISSN: 15329356     Source Type: Journal    
DOI: 10.1080/07362994.2010.482827     Document Type: Article

References (11)

1. Barrieu, P., and El Karoui, N. 2004. Optimal Derivatives Design Under Dynamic Risk Measures, Contemporary Mathematics. Vol. 351. Amer. Math. Soc., Providence, RI.
2. Briand, P., Coquet, F., Hu, Y., Mémin, J., and Peng, S. 2000. A converse comparison theorem for BSDEs and related properties of g-expectation. Electron. Comm. Probab. 5:101-117. (electronic)
3. Coquet, F., Hu, Y., Mémin, J., and Peng, S. 2002. Filtration-consistent nonlinear expectations and related g-expectations. Probab. Theory Related Fields 123(1):1-27.
4. Hu, Y., Imkeller, P., and Müller, M. 2005. Utility maximization in incomplete markets. Ann. Appl. Probab. 15(3):1691-1712.
5. Hu, Y., Ma, J., Peng, S., and Yao, S. 2008. Representation theorems for quadratic Fconsistent nonlinear expectations. Stochastic Process. Appl. 118(9): 1518-1551.
6. Kazamaki, N. 1994. Continuous Exponential Martingales and BMO, Lecture Notes in Mathematics, Vol. 1579. Springer-Verlag, Berlin.
7. Kobylanski, M. 2000. Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab. 28(2):558-602.
8. Peng, S. 1997. Backward SDE and Related g-Expectation, Pitman Res. Notes Math. Ser., Vol. 364. Longman, Harlow.
9. Peng, S. 2004. Nonlinear Expectations, Nonlinear Evaluations and Risk Measures, Lecture Notes in Math., Vol. 1856 Springer, Berlin.
10. Protter, P. 1990. Stochastic Integration and Differential Equations, Applications of Mathematics (New York), Vol. 21. Springer-Verlag, Berlin.
11. Tyrrell Rockafellar, R. 1970. Convex Analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, NJ.