Open Access
Issue
ESAIM: PS
Volume 25, 2021
Page(s) 133 - 203
DOI https://doi.org/10.1051/ps/2021006
Published online 23 March 2021
  1. Y. Ait-Sahalia and J. Jacod, High-Frequency Financial Econometrics. Princeton University Press, 1 edition (2014). [Google Scholar]
  2. Y. Aït-Sahalia and J. Jacod, Semimartingale: Itô or not? Stochastic Process. Appl. 128 (2018) 233–254. [Google Scholar]
  3. V. Anh and J. Yong, Backward stochastic Volterra integral equations in Hilbert spaces. In Differential & difference equations and applications. Hindawi Publ. Corp., New York (2006) 57–66. [Google Scholar]
  4. D. Becherer, Bounded solutions to backward SDE’s with jumps for utility optimization and indifference hedging. Ann. Appl. Probab. 16 (2006) 2027–2054. [Google Scholar]
  5. M.A. Berger and V.J. Mizel, Volterra equations with Itô integrals. I. J. Integral Equ. 2 (1980) 187–245. [Google Scholar]
  6. M.A. Berger and V.J. Mizel, Volterra equations with Itô integrals. II. J. Integr. Equ. 2 (1980) 319–337. [Google Scholar]
  7. N. Bouleau and L. Denis, Dirichlet forms methods for Poisson point measures and Lévy processes. With emphasis on the creation-annihilation techniques. Vol. 76 of Probability Theory and Stochastic Modelling. Springer, Cham (2015). [Google Scholar]
  8. Ph. Briand, B. Delyon, Y. Hu, E. Pardoux and L. Stoica, Lp solutions of backward stochastic differential equations. Stochastic Process. Appl. 108 (2003) 109–129. [Google Scholar]
  9. F. Confortola, M. Fuhrman and J. Jacod, Backward stochastic differential equation driven by a marked point process: an elementary approach with an application to optimal control. Ann. Appl. Probab. 26 (2016) 1743–1773. [Google Scholar]
  10. C. Dellacherie and P.-A. Meyer, Probabilités et potentiel. Théorie des martingales. Chapitres V à VIII. Hermann, Paris (1980). [Google Scholar]
  11. Ł. Delong, Backward stochastic differential equations with jumps and their actuarial and financial applications. BSDEs with jumps. European Actuarial Academy (EAA) Series. Springer, London (2013). [Google Scholar]
  12. G. Di Nunno, B. Øksendal and F. Proske, Malliavin calculus for Lévy processes with applications to finance. Universitext. Springer-Verlag, Berlin (2009). [Google Scholar]
  13. J. Djordjević and S. Janković, On a class of backward stochastic Volterra integral equations. Appl. Math. Lett. 26 (2013) 1192–1197. [Google Scholar]
  14. J. Djordjević and S. Janković, Backward stochastic Volterra integral equations with additive perturbations. Appl. Math. Comput. 265 (2015) 903–910. [Google Scholar]
  15. N. El Karoui and S.-J. Huang, A general result of existence and uniqueness of backward stochastic differential equations. In Backward stochastic differential equations (Paris, 1995–1996). Volume 364 of Pitman Res. Notes Math. Ser. Longman, Harlow (1997) 27–36. [Google Scholar]
  16. N. El Karoui, S.G. Peng and M.C. Quenez, Backward stochastic differential equations in finance. Math. Finance 7 (1997) 1–71. [Google Scholar]
  17. Y. Hu and B. Øksendal, Linear Volterra backward stochastic integral equations. Stochastic Process. Appl. 129 (2019) 626–633. [Google Scholar]
  18. J. Jacod, Calcul stochastique et problèmes de martingales. Vol. 714 of Lecture Notes in Mathematics. Springer, Berlin (1979). [Google Scholar]
  19. J. Jacod and A.N. Shiryaev, Limit theorems for stochastic processes. Vol. 288 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition (2003). [Google Scholar]
  20. A.M. Kolodiĭ, Existence of solutions of stochastic Volterra integral equations. In Theory of random processes, No. 11. “ Naukova Dumka”, Kiev (1983) 51–57. [Google Scholar]
  21. A.M. Kolodiĭ, Existence of solutions of stochastic integral equations of Itô-Volterra type with locally integrable and continuous trajectories. In Theory of random processes, No. 12. “ Naukova Dumka”, Kiev (1984) 32–40. [Google Scholar]
  22. S.G. Kreĭn, Yu. Ī. Petunīn and E.M. Semënov, Interpolation of linear operators. Translated from the Russian by J. Szűcs. Vol. 54 of Translations of Mathematical Monographs. American Mathematical Society, Providence, R.I. (1982). [Google Scholar]
  23. T. Kruse and A. Popier, Bsdes with monotone generator driven by Brownian and Poisson noises in a general filtration. Stochastics 88 (2016) 491–539. [Google Scholar]
  24. T. Kruse and A. Popier, Lp-solution for BSDEs with jumps in the case p < 2: corrections to the paper ‘BSDEs with monotone generator driven by Brownian and Poisson noises in a general filtration. Stochastics 89 (2017) 1201–1227. [Google Scholar]
  25. E. Lenglart, D. Lépingle and M. Pratelli, Présentation unifiée de certaines inégalités de la théorie des martingales. With an appendix by Lenglart. In Seminar on Probability, XIV (Paris, 1978/1979) (French). Vol. 784 of Lecture Notes in Math. Springer, Berlin (1980) 26–52. [Google Scholar]
  26. J. Lin, Adapted solution of a backward stochastic nonlinear Volterra integral equation. Stochastic Anal. Appl. 20 (2002) 165–183. [Google Scholar]
  27. P. Lin and J. Yong, Controlled singular volterra integral equations and pontryagin maximum principle. SIAM J. Control Optim. 58 (2020) 136–164. [Google Scholar]
  28. W. Lu, Backward stochastic Volterra integral equations associated with a Levy process and applications. Preprint arXiv:1106.6129 (2011). [Google Scholar]
  29. C. Marinelli and M. Röckner, On maximal inequalities for purely discontinuous martingales in infinite dimensions. In Séminaire de Probabilités XLVI. Vol. 2123 of Lecture Notes in Math. Springer, Cham (2014) 293–315. [Google Scholar]
  30. L. Overbeck and J.A.L. Röder, Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle. Probab. Uncertain. Quant. Risk 3 (2018) 4. [Google Scholar]
  31. A. Papapantoleon, D. Possamaï and A. Saplaouras, Existence and uniqueness results for BSDE with jumps: the whole nine yards. Electr. J. Probab. 23 (2018) EJP240. [Google Scholar]
  32. E. Pardoux and S.G. Peng, Adapted solution of a backward stochastic differential equation. Systems Control Lett. 14 (1990) 55–61. [Google Scholar]
  33. E. Pardoux and P. Protter, Stochastic Volterra equations with anticipating coefficients. Ann. Probab. 18 (1990) 1635–1655. [Google Scholar]
  34. E. Pardoux and A. Rascanu, Stochastic Differential Equations, Backward SDEs, Partial Differential Equations. Vol. 69 of Stochastic Modelling and Applied Probability. Springer-Verlag (2014). [Google Scholar]
  35. P.E. Protter, Volterra equations driven by semimartingales. Ann. Probab. 13 (1985) 519–530. [Google Scholar]
  36. P.E. Protter, Stochastic integration and differential equations. Vol. 21 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin, second edition (2004). [Google Scholar]
  37. Y. Ren, On solutions of backward stochastic Volterra integral equations with jumps in Hilbert spaces. J. Optim. Theory Appl. 144 (2010) 319–333. [Google Scholar]
  38. D. Revuz and M. Yor, Continuous martingales and Brownian motion. Vol. 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, third edition (1999). [Google Scholar]
  39. R. Situ, Theory of stochastic differential equations with jumps and applications. Mathematical and Analytical Techniques with Applications to Engineering. Springer, New York (2005). [Google Scholar]
  40. H. Wang, J. Sun and J. Yong, Recursive Utility Processes, Dynamic Risk Measures and Quadratic Backward Stochastic Volterra Integral Equations. Preprint arXiv:1810.10149 (2018). [Google Scholar]
  41. T. Wang, Lp solutions of backward stochastic Volterra integral equations. Acta Math. Sin. (Engl. Ser.) 28 (2012) 1875–1882. [Google Scholar]
  42. T. Wangand J. Yong, Comparison theorems for some backward stochastic Volterra integral equations. Stochastic Process. Appl. 125 (2015) 1756–1798. [Google Scholar]
  43. T. Wang and J. Yong, Backward stochastic Volterra integral equations—representation of adapted solutions. Stochastic Process. Appl. 129 (2019) 4926–4964. [Google Scholar]
  44. Z. Wang and X. Zhang, Non-Lipschitz backward stochastic Volterra type equations with jumps. Stoch. Dyn. 7 (2007) 479–496. [Google Scholar]
  45. J. Yong, Backward stochastic Volterra integral equations and some related problems. Stochastic Process. Appl. 116 (2006) 779–795. [Google Scholar]
  46. J. Yong, Well-posedness and regularity of backward stochastic Volterra integral equations. Probab. Theory Related Fields 142 (2008) 21–77. [Google Scholar]
  47. J. Yong, Backward stochastic Volterra integral equations—a brief survey. Appl. Math. J. Chinese Univ. Ser. B 28 (2013) 383–394. [Google Scholar]

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