Open Access
Issue |
ESAIM: PS
Volume 28, 2024
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Page(s) | 1 - 21 | |
DOI | https://doi.org/10.1051/ps/2023019 | |
Published online | 12 January 2024 |
- J.M. Bismut, Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl. 44 (1973) 384–404. [CrossRef] [MathSciNet] [Google Scholar]
- E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14 (1990) 55–61. [CrossRef] [Google Scholar]
- N. El Karoui, C. Kapoudjian, E. Pardoux, S. Peng and M.C. Quenez, Reflected solutions of backward SDE’s and related obstacle problems for PDE’s. Ann. Probab. 25 (1997) 702–737. [CrossRef] [MathSciNet] [Google Scholar]
- S. Hamadéne, Reflected BSDE’s with discontinuous barrier and application. Stochastics. 74 (2002) 571–596. [Google Scholar]
- J.P. Lepeltier and M. Xu, Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier. Statist. Probab. Lett. 75 (2005) 58–66. [CrossRef] [MathSciNet] [Google Scholar]
- H. O, M.-C. Kim and K.-G. Kim, Dynamic programming approach to reflected backward stochastic differential equations. Preprint (2020). [Google Scholar]
- 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) 827–852. [CrossRef] [MathSciNet] [Google Scholar]
- H.M. Soner, N. Touzi and J. Zhang, Wellposedness of second order backward SDEs. Probab. Theory Related Fields 153 (2012) 149–190. [CrossRef] [MathSciNet] [Google Scholar]
- D. Possamaï, X. Tan and C. Zhou, Stochastic control for a class of nonlinear kernels and applications. Ann. Probab. 46 (2018) 551–603. [MathSciNet] [Google Scholar]
- A. Matoussi, D. Possamaï and C. Zhou, Second order reflected backward stochastic differential equations. Ann. Appl. Probab. 23 (2013) 2420–2457. [CrossRef] [MathSciNet] [Google Scholar]
- A. Matoussi, D. Possamaï and C. Zhou, Corrigendum for “Second–order reflected backward stochastic differential equations” and “Second–order BSDEs with general reflection and game options under uncertainty”. Preprint arXiv:1706.08588 (2020). [Google Scholar]
- F. Noubiagain, Contribution aux équations différentielles stochastiques rétrogrades réfléchies du second ordre, Ph.D. Thesis. Université du Maine and Université Bretagne Loire, France (2017). [Google Scholar]
- S. Peng, Nonlinear expectations and stochastic calculus under uncertainty. Preprint arXiv:1002.4546 (2010). [Google Scholar]
- M. Hu, S. Ji, S. Peng and Y. Song, Backward stochastic differential equation driven by G-Brownian motion. Stochastic. Process. Appl. 124 (2014) 759–784. [CrossRef] [MathSciNet] [Google Scholar]
- H. Li, S. Peng and A. Soumana Himma, Reflected solutions of BSDEs driven by G-Brownian motion. Sci. China. Math. 61 (2018) 1–26. [MathSciNet] [Google Scholar]
- A. Soumana Hima, Équations différentielles stochastiques sous G-espérance et applications, Ph.D. Thesis. Université de Rennes 1, France (2017). [Google Scholar]
- M. Nutz and R. van Handel, Constructing sublinear expectations on path space. Stochastic Process. Appl. 123 (2013) 3100–3121. [CrossRef] [MathSciNet] [Google Scholar]
- R. Karandikar, On pathwise stochastic integration. Stochastic Process. Appl. 57 (1995) 11–18. [CrossRef] [MathSciNet] [Google Scholar]
- D.W. Stroock and S.R.S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, Berlin (1979). [Google Scholar]
- N. El Karoui and X. Tan, Capacities, measurable selection and dynamic programming part II: application in stochastic control problems. Preprint arXiv:1310.3364 (2013). [Google Scholar]
- M. Nutz, Pathwise construction of stochastic integrals. Electron. Commun. Probab. 17 (2012) 1–7. [CrossRef] [Google Scholar]
- B. Bouchard, D. Possamaï, X. Tan and C. Zhou, A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations. Ann. Inst. H. Poincaré Probab. Statist. 54 (2018) 154–172. [CrossRef] [Google Scholar]
- S. Fan, Existence, uniqueness and approximation for Lp-solutions of reflected BSDEs with generators of one-sided Osgood type. Acta Math. Sin. Engl. Ser. 33 (2017) 807–838. [CrossRef] [MathSciNet] [Google Scholar]
- H. O, M.-C. Kim and C.-G. Pak, Representation of solutions to 2BSDEs in an extended monotonicity setting. Bull. Sci. Math. 164 (2020) 102907. [CrossRef] [MathSciNet] [Google Scholar]
- J. Neveu, Discrete Parameter Martingales, revised edn. North-Holland Publishing Company, Amsterdam (1975). [Google Scholar]
- N. El Karoui, E. Pardoux and M.C. Quenez, Reflected backward SDEs and American options, in Numerical Methods in Finance, Publications of the Newton Institute. Cambridge University Press, Cambridge (1997) 215–231. [CrossRef] [Google Scholar]
- M.C. Quenez and A. Sulem, Reflected BSDEs and robust optimal stopping for dynamic risk measures with jumps. Stochastic Process. Appl. 124 (2014) 3031–3054. [CrossRef] [MathSciNet] [Google Scholar]
- N. El Karoui, S. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [Google Scholar]
- M. Nutz, Robust superhedging with jumps and diffusion. Stochastic Process. Appl. 125 (2015) 4543–4555. [CrossRef] [MathSciNet] [Google Scholar]
- I. Ekren, Viscosity solutions of obstacle problems for fully nonlinear path-dependent PDEs. Stochastic Process. Appl. (to appear). http://dx.doi.org/10.1016/j.spa.2017.03.016 [Google Scholar]
- A. Matoussi, L. Piozin and D. Possamaï, Second order BSDEs with general reflection and game options under uncertainty. Stochastic Process. Appl. 124 (2014) 2281–2321. [CrossRef] [MathSciNet] [Google Scholar]
- H. Li and S. Peng, Reflected backward stochastic differential equation driven by G-Brownian motion with an upper obstacle. Stochastic Process. Appl. (to appear). [Google Scholar]
- H. Li and Y. Song, Backward stochastic differential equations driven by G-Brownian motion with double reflections. J. Theoret. Probab. (to appear). https://doi.org/10.1007/s10959-020-01038-5 [Google Scholar]
- T. Pham and J. Zhang, Some norm estimates for semimartingales. Electron. J. Probab. 18 (2013) 1–25. [CrossRef] [Google Scholar]
- M. Nutz and J. Zhang, Optimal stopping under adverse nonlinear expectation and related games. Ann. Appl. Probab. 25 (2015) 2503–2534. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin Heidelberg New York (1987). [CrossRef] [Google Scholar]
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