Free Access
Issue
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
Page(s) 1107 - 1133
DOI https://doi.org/10.1051/m2an/2010054
Published online 26 August 2010
  1. V. Bally and G. Pagès, Error analysis of the quantization algorithm for obstacle problems. Stochastic Processes their Appl. 106 (2003) 1–40. [Google Scholar]
  2. V. Bally and G. Pagès, A quantization algorithm for solving multi dimensional discrete-time optional stopping problems. Bernoulli 6 (2003) 1003–1049. [CrossRef] [MathSciNet] [Google Scholar]
  3. D. Becherer, Bounded solutions to backward SDE's with jumps for utility optimization and indifference pricing. Ann. Appl. Prob. 16 (2006) 2027–2054. [CrossRef] [Google Scholar]
  4. J.M. Bismut, Théorie probabiliste du contrôle des diffusions, Mem. Amer. Math. Soc. 176. Providence, Rhode Island (1973). [Google Scholar]
  5. B. Bouchard and N. Touzi, Discrete time approximation and Monte Carlo simulation for Backward Stochastic Differential Equations. Stochastic Processes their Appl. 111 (2004) 175–206. [CrossRef] [Google Scholar]
  6. B. Bouchard, I. Ekeland and N. Touzi, On the Malliavin approach to Monte Carlo methods of conditional expectations. Financ. Stoch. 8 (2004) 45–71. [CrossRef] [Google Scholar]
  7. P. Briand and Y. Hu, BSDE with quadratic growth and unbounded terminal value. Probab. Theor. Relat. Fields 136 (2006) 604–618. [CrossRef] [Google Scholar]
  8. K.-T. Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula. Ann. Math. 65 (1957) 163–178. [CrossRef] [MathSciNet] [Google Scholar]
  9. P. Cheridito, M. Soner, N. Touzi and N. Victoir, Second-order backward stochastic differential equations and fully non linear parabolic pdes. Commun. Pure Appl. Math. 60 (2007) 1081–1110. [CrossRef] [MathSciNet] [Google Scholar]
  10. D. Crisan and K. Manolarakis, Numerical solution for a BSDE using the Cubature method. Preprint available at http://www2.imperial.ac.uk/ dcrisan/ (2007). [Google Scholar]
  11. D. Crisan, K. Manolarakis and N. Touzi, On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights. Stochastic Processes their Appl. 120 (2010) 1133–1158. [CrossRef] [Google Scholar]
  12. J. Cvitanic and I. Karatzas, Hedging contingent claims with constrained portfolios. Ann. Appl. Prob. 3 (1993) 652–681. [CrossRef] [MathSciNet] [Google Scholar]
  13. D. Duffy and L. Epstein, Asset pricing with stochastic differential utility. Rev. Financ. Stud. 5 (1992) 411–436. [CrossRef] [Google Scholar]
  14. D. Duffy and L. Epstein, Stochastic differential utility. Econometrica 60 (1992) 353–394. [CrossRef] [MathSciNet] [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, N. El Karoui and L. Mazliak Eds., Longman (1996). [Google Scholar]
  16. N. El Karoui and M. Quenez, Dynamic programming and pricing of contigent claims in incomplete markets. SIAM J. Contr. Opt. 33 (1995) 29–66. [CrossRef] [Google Scholar]
  17. N. El Karoui and M. Quenez, Non linear pricing theory and Backward Stochastic Differential Equations, in Financial Mathematics 1656, Springer (1995) 191–246. [Google Scholar]
  18. N. El Karoui, C. Kapoudjan, E. Pardoux, S. Peng and M.C. Quenez, Reflected solutions of backward SDEs and related obstacle problems. Annals Probab. 25 (1997) 702–737. [CrossRef] [MathSciNet] [Google Scholar]
  19. N. El Karoui, E. Pardoux and M. Quenez, Reflected backward SDEs and American Options, in Numerical Methods in Finance, Chris Rogers and Denis Talay Eds., Cambridge University Press, Cambridge (1997). [Google Scholar]
  20. N. El Karoui, S. Peng and M. Quenez, Backward Stochastic Differential Equations in finance. Mathematical Finance 7 (1997) 1–71. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Feynman, Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20 (1948) 367–387. [CrossRef] [MathSciNet] [Google Scholar]
  22. H. Föllmer and A. Schied, Convex measures of risk and trading constraints. Financ. Stoch. 6 (2002) 429–447. [CrossRef] [Google Scholar]
  23. P. Friz and N. Victoir, Multidimensional Stochastic Processes as Rough Paths: Theory and applications. Cambridge studies in advanced mathematics, Cambridge University Press, Cambridge (2010). [Google Scholar]
  24. E. Gobet and C. Labart, Error expansion for the discretization of Backward Stochastic Differential Equations. Stochastic Processes their Appl. 117 (2007) 803–829. [CrossRef] [Google Scholar]
  25. E. Gobet, J.P. Lemor and X. Warin, A regression based Monte Carlo method to solve Backward Stochastic Differential Equations. Ann. Appl. Prob. 15 (2005) 2172–2202. [CrossRef] [Google Scholar]
  26. E. Gobet, J.P. Lemor 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]
  27. E. Jouini and H. Kallal, Arbitrage in securities markets with short sales constraints. Mathematical Finance 5 (1995) 178–197. [Google Scholar]
  28. M. Kac, On distributions of certain Wiener functionals. Trans. Amer. Math. Soc. 65 (1949) 1–13. [CrossRef] [MathSciNet] [Google Scholar]
  29. I. Karatzas and S. Schreve, Brownian Motion and Stochastic Calculus. Springer Verlag, New York (1991). [Google Scholar]
  30. M. Kobylanski, Backward Stochastic Differential Equations and Partial Differential Equations. Ann. Appl. Prob. 28 (2000) 558–602. [Google Scholar]
  31. J.-P. Lepeltier and J. San Martin, Backward Stochastic Differential Equations with continuous coefficients. Stat. Probab. Lett. 32 (1997) 425–430. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  32. F. Longstaff and E.S. Schwartz, Valuing American options by simulation: a simple least squares approach. Rev. Financ. Stud. 14 (2001) 113–147. [CrossRef] [Google Scholar]
  33. T. Lyons and Z. Qian, System Control and Rough Paths. Oxford Science publication, Oxford University Press, Oxford (2002). [Google Scholar]
  34. T. Lyons and N. Victoir, Cubature on Wiener space. Proc. Royal Soc. London 468 (2004) 169–198. [Google Scholar]
  35. T. Lyons, M. Caruana and T. Levy, Differential Equations Driven by Rough Paths, Lecture Notes in Mathematics 1908. Springer (2004). [Google Scholar]
  36. J. Ma and J. Zhang, Representation theorems for Backward Stochastic Differential Equations. Ann. Appl. Prob. 12 (2002) 1390–1418. [CrossRef] [Google Scholar]
  37. J. Ma and J. Zhang, Representation and regularities for solutions to BSDEs with reflections. Stochastic Processes their Appl. 115 (2005) 539–569. [CrossRef] [Google Scholar]
  38. J. Ma, P. Protter and J. Yong, Solving Forward-Backward SDEs expicitly – A four step scheme. Probab. Theor. Relat. Fields 122 (1994) 163–190. [Google Scholar]
  39. D. Nualart, The Malliavin calculus and related topics. Springer-Verlag (1996). [Google Scholar]
  40. E. Pardoux and S. Peng, Adapted solution to Backward Stochastic Differential Equations. Syst. Contr. Lett. 14 (1990) 55–61. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  41. E. Pardoux and S. Peng, Backward Stochastic Differential Equations and quasi linear parabolic partial differential equations, in Lecture Notes in Control and Information Sciences 176, Springer, Berlin/Heidelberg (1992) 200–217. [Google Scholar]
  42. E. Pardoux and S. Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs. Probab. Theor. Relat. Fields 114 (1999) 123–150. [CrossRef] [MathSciNet] [Google Scholar]
  43. S. Peng, Backward SDEs and related g-expectations, in Pitman Research Notes in Mathematics Series 364, Longman, Harlow (1997) 141–159. [Google Scholar]
  44. S. Peng, Non linear expectations non linear evaluations and risk measures 1856. Springer-Verlag (2004). [Google Scholar]
  45. S. Peng, Modelling derivatives pricing mechanisms with their generating functions. Preprint, arxiv:math/0605599v1 (2006). [Google Scholar]
  46. E. Rosazza Giannin, Risk measures via g expectations. Insur. Math. Econ. 39 (2006) 19–34. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  47. S. Tang and X. Li, Necessary conditions for optimal control of stochastic systems with random jumps. SIAM J. Contr. Opt. 32 (1994) 1447–1475. [CrossRef] [MathSciNet] [Google Scholar]
  48. J. Zhang, Some fine properties of backward stochastic differential equations. Ph.D. Thesis, Purdue University, USA (2001). [Google Scholar]
  49. J. Zhang, A numerical scheme for BSDEs. Ann. Appl. Prob. 14 (2004) 459–488. [CrossRef] [MathSciNet] [Google Scholar]

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