Free Access
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
Page(s) 1107 - 1133
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. [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. [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. [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 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. [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. [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. [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. [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. [CrossRef] [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. [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. [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. [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. [CrossRef] [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. [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. [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.

Recommended for you