Open Access
Issue |
ESAIM: PS
Volume 27, 2023
|
|
---|---|---|
Page(s) | 19 - 79 | |
DOI | https://doi.org/10.1051/ps/2022017 | |
Published online | 06 January 2023 |
- N. Agram, Dynamic risk measure for BSVIE with jumps and semimartingale issues. Stoch. Anal. Appl. 37 (2019) 361-376. [CrossRef] [MathSciNet] [Google Scholar]
- V. Bally and G. Pagès, Error analysis of the optimal quantization algorithm for obstacle problems. Stoch. Process. Appl. 106 (2003) 1-40. [CrossRef] [Google Scholar]
- P. Beissner and E. Rosazza Gianin, The term structure of Sharpe ratios and arbitrage-free asset pricing in continuous time. Probab. Uncertain. Quantit. Risk 6 (2021) 23-52. [CrossRef] [Google Scholar]
- C. Bender and R. Denk, A forward scheme for backward SDEs. Stoch. Process. Appl. 117 (2007) 1793-1812. [CrossRef] [Google Scholar]
- C. Bender and S. Pokalyuk, Discretization of backward stochastic Volterra integral equations. In Recent Developments in Computational Finance: Foundations, Algorithms and Applications. (2013) 245-278. [Google Scholar]
- M.A. Berger and V.J. Mizel, Volterra equations with Ito integrals-I. J. Int. Eqs. 2 (1980) 187-245. [Google Scholar]
- J.M. Bismut, An introductory approach to duality in optimal stochastic control. SIAM Rev. 20 (1978) 62-78. [CrossRef] [MathSciNet] [Google Scholar]
- B. Bouchard and N. Touzi, Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations. Stoch. Process. Appl. 111 (2004) 175-206. [CrossRef] [Google Scholar]
- P. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica, Lp solutions of backward stochastic differential equations. Stoch. Process. Appl. 108 (2003) 109-129. [CrossRef] [Google Scholar]
- P. Briand, B. Delyon and J. Mémin, Donsker-type theorem for BSDEs. Electron. Commun. Probab. 6 (2001) 1-14. (2007) [CrossRef] [Google Scholar]
- F. Delarue and S. Menozzi, A forward-backward stochastic algorithm for quasi-linear PDEs. Ann. Appl. Probab. 16 (2006) 140-184. [CrossRef] [MathSciNet] [Google Scholar]
- J. Douglas, J. Ma and P. Protter, Numerical methods for forward-backward stochastic differential equations. Ann. Appl. Probab. 6 (1996) 940-968. [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]
- E. Gobet and C. Labart, Error expansion for the discretization of backward stochastic differential equations. Stoch. Process. Appl. 117 (2007) 803-829. [CrossRef] [Google Scholar]
- E. Gobet and J.P. Lemor, Numerical simulation of BSDEs using empirical regression methods: theory and practice. preprint. arXiv:0806.4447. [Google Scholar]
- E. Gobet, J.P. Lemor and X. Warin, A regression-based Monte Carlo method to solve backward stochastic differential equations. Ann. Appl. Probab. 15 (2005) 2172-2202. [CrossRef] [MathSciNet] [Google Scholar]
- E. Gobet and A. Makhlouf, L2-time regularity of BSDEs with irregular terminal functions. Stoch. Process. Appl. 120 (2010) 1105-1132. [CrossRef] [Google Scholar]
- Y. Hamaguchi, Extended backward stochastic Volterra integral equations and their applications to time-inconsistent stochastic recursive control problems. Math. Control Relat. Fields 11 (2021) 197-242. [CrossRef] [Google Scholar]
- Y. Hamaguchi, Infinite horizon backward stochastic Volterra integral equations and discounted control problems. ESAIM: COCV 101 (2021) 47 pages. [Google Scholar]
- P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations. Springer (1992). [Google Scholar]
- E. Kromer and L. Overbeck, Differentiability of BSVIEs and dynamic capital allocations. Int. J. Theor. Appi. Finance 20 (2017) 1-26. [Google Scholar]
- J.P. Lemor, E. Gobet and X. Warin, Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations. Bernoulli 12 (2006) 889-916. [CrossRef] [MathSciNet] [Google Scholar]
- J. Lin, Adapted solution of a backward stochastic nonlinear Volterra integral equation. Stoch. Anal. Appi. 20 (2002) 165-183. [CrossRef] [Google Scholar]
- A. Lionnet, G. Dos Reis and L. Szpruch, Convergence and qualitative properties of modified explicit schemes for BSDEs with polynomial growth. Ann. Appi. Probab. 28 (2018) 2544-2591. [Google Scholar]
- T. Nakayama, Approximation of BSDE’s by stochastic difference equation’s. J. Math. Sci. Univ. Tokyo 9 (2002) 257-278. [MathSciNet] [Google Scholar]
- D. Nualart, The Mallivain Calculus and Related Topics, Second Edition. Springer (2006). [Google Scholar]
- E. Pardoux and S.G. Peng, Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990) 55-61. [Google Scholar]
- E. Pardoux and S. Peng, Backward stochastic differential equations and quasilinear parabolic partial differential equations. In Stochastic partial differential equations and their applications. 200-217 Springer, Berlin, Heidelberg (1992). [CrossRef] [Google Scholar]
- S. Peng and M. Xu, Numerical algorithms for backward stochastic differential equations with 1-d Brownian motion: Convergence and simulations. ESAIM Math. Model. Numer. Anal. 45 (2011) 335-360. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- A. Popier, Backward stochastic Volterra integral equations with jumps in a general filtration. ESAIM: PS 25 (2021) 133-203. [CrossRef] [EDP Sciences] [Google Scholar]
- Y. Shi and T. Wang, Solvability of general backward stochastic Volterra integral equations. J. Korean Math. Soc. 49 (2012) 1301-1321. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Shi, T. Wang and J. Yong, Mean-field backward stochastic Volterra integral equations. Discrete Contin. Dyn. Syst. 18 (2013) 1929-1967. [Google Scholar]
- Y. Shi, T. Wang and J. Yong, Optimal control problems of forward-backward stochastic Volterra integral equations. Math. Control Relat. Fields 5 (2015) 613-649. [Google Scholar]
- H. Wang, Extended backward stochastic Volterra integral equations, quasilinear parabolic equations, and Feynman-Kac formula. Stoch. Dyn. 21 (2021) 2150004. [CrossRef] [Google Scholar]
- H. Wang, J. Sun and J. Yong, Recursive utility processes, dynamic risk measures and quadratic backward stochastic Volterra integral equations. App. Math. Optim. 84 (2021) 145-190 [CrossRef] [MathSciNet] [Google Scholar]
- H. Wang and J. Yong, Time-inconsistent stochastic optimal control problems and backward stochastic Volterra integral equations. ESAIM: COCV 27 (2021) 40. [CrossRef] [EDP Sciences] [Google Scholar]
- H. Wang, J. Yong and J. Zhang, Path dependent Feynman-Kac formula for forward backward stochastic Volterra integral equations. Ann. Inst. Henri Poincaré Probab. Stat. 58 (2022) 603-638. [CrossRef] [MathSciNet] [Google Scholar]
- T. Wang, L p solutions of backward stochastic Volterra integral equations. Acta Math. Sinica 28 (2012) 1875-1882. [CrossRef] [MathSciNet] [Google Scholar]
- T. Wang and J. Yong, Backward stochastic Volterra integral equations-representation of adapted solutions. Stoch. Process. Appl. 129 (2019) 4926-4964. [CrossRef] [Google Scholar]
- T. Wang and H. Zhang, Optimal control problems of forward-backward stochastic Volterra integral equations with closed control regions. SIAM J. Control Optim. 55 (2017) 2574-2602. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Wang, A numerical scheme for BSVIEs. preprint. arXiv:1605.04865. [Google Scholar]
- J. Yong, Backward stochastic Volterra integral equations and some related problems. Stoch. Anal. Appl. 116 (2006) 779-795. [Google Scholar]
- J. Yong, Continuous-time dynamic risk measures by backward stochastic Volterra integral equations. Appl. Anal. 86 (2007) 1429-1442. [CrossRef] [MathSciNet] [Google Scholar]
- J. Yong, Well-posedness and regularity of backward stochastic Volterra integral equations. Probab. Theory Related Fields 142 (2008) 2-77. [Google Scholar]
- J. Yong, Time-inconsistent optimal control problems and the equilibrium HJB equation. Math. Control Relat. Fields 2 (2012) 271-329. [Google Scholar]
- J. Zhang, A numerical scheme for BSDEs. Ann. Appl. Probab. 14 (2004) 459-488. [Google Scholar]
- J. Zhang, Backward Stochastic Differential Equations; From Linear to Fully Nonlinear Theory. Springer (2017). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.