Abstract
We investigate nonlinear expectations. We briefly discuss Choquet expectations and we focus on g-expectations defined by BSDEs. The connection between filtration-consistent nonlinear expectations and g-expectations is presented. We study the properties of translation invariance, positive homogeneity, convexity and sub-linearity of g-expectations and we show that these properties are determined by the generator of the BSDE defining the g-expectation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chen, Z., Kulperger, R.: Minimax pricing and Choquet expectations. Insur. Math. Econ. 38, 518–528 (2006)
Chen, Z., Chen, T., Davison, M.: Choquet expectation and Peng’s g-expectations. Ann. Probab. 33, 1179–1199 (2005)
Choquet, G.: Theory of capacities. Ann. Inst. Fourier 5, 131–195 (1953)
Cohen, S.N.: Representing filtration consistent non-linear expectations as g-expectations in general probability spaces. Preprint (2011)
Coquet, F., Hu, Y., Mémin, J., Peng, S.: Filtration-consistent non-linear expectations and related g-expectations. Probab. Theory Relat. Fields 123, 1–27 (2002)
Jiang, L.: Convexity, translation invariance and subadditivity for g-expectations and related risk measures. Ann. Appl. Probab. 18, 245–258 (2008)
Nguyen, H., Pham, U., Tran, H.: On some claims related to Choquet integral risk measures. Ann. Oper. Res. 195, 5–31 (2012)
Peng, S.: Backward SDE and related g-expectations. In: El Karoui, N., Mazliak, L. (eds.) Backward Stochastic Differential Equations, Pitman Research Notes, pp. 141–161. Pitman, London (1997)
Rosazza Gianin, E.: Risk measures via g-expectations. Insur. Math. Econ. 39, 19–34 (2006)
Royer, M.: Backward stochastic differential equations with jumps and related non-linear expectations. Stoch. Process. Appl. 116, 1358–1376 (2006)
Wang, S.: A class of distortion operators for pricing financial and insurance risks. J. Risk Insur. 1, 15–36 (2000)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Delong, Ł. (2013). Nonlinear Expectations and g-Expectations. In: Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications. EAA Series. Springer, London. https://doi.org/10.1007/978-1-4471-5331-3_6
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5331-3_6
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5330-6
Online ISBN: 978-1-4471-5331-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)