- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 753025, 13 pages
Terminal-Dependent Statistical Inference for the Integral Form of FBSDE
1School of Mathematics, Shandong University, Jinan 250100, China
2College of Mathematics, Qingdao University, Qingdao 266071, China
Received 14 June 2013; Revised 4 September 2013; Accepted 22 September 2013
Academic Editor: Vasile Dragan
Copyright © 2013 Qi Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. M. Bismut, “Conjugate convex functions in optimal stochastic control,” Journal of Mathematical Analysis and Applications, vol. 44, pp. 384–404, 1973.
- É. Pardoux and S. G. Peng, “Adapted solution of a backward stochastic differential equation,” Systems & Control Letters, vol. 14, no. 1, pp. 55–61, 1990.
- S. G. Peng, “Probabilistic interpretation for systems of quasilinear parabolic partial differential equations,” Stochastics and Stochastics Reports, vol. 37, no. 1-2, pp. 61–74, 1991.
- É. Pardoux and S. Peng, “Backward stochastic differential equations and quasilinear parabolic partial differential equations,” Stochastic Partial Differential Equations and Their Applications, Springer, vol. 176, pp. 200–217, 1992.
- É. Pardoux and S. Tang, “Forward-backward stochastic differential equations and quasilinear parabolic PDEs,” Probability Theory and Related Fields, vol. 114, no. 2, pp. 123–150, 1999.
- S. Peng and Z. Wu, “Fully coupled forward-backward stochastic differential equations and applications to optimal control,” SIAM Journal on Control and Optimization, vol. 37, no. 3, pp. 825–843, 1999.
- J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, vol. 1702 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1999.
- D. Nualart and W. Schoutens, “Backward stochastic differential equations and Feynman-Kac formula for Lévy processes, with applications in finance,” Bernoulli, vol. 7, no. 5, pp. 761–776, 2001.
- D. Duffie and L. G. Epstein, “Stochastic differential utility,” Econometrica, vol. 60, no. 2, pp. 353–394, 1992.
- N. El Karoui and M. C. Quenez, “Dynamic programming and pricing of contingent claims in an incomplete market,” SIAM Journal on Control and Optimization, vol. 33, no. 1, pp. 29–66, 1995.
- L. Lin, F. Li, L. Zhu, and W. K. Härdle, “Mean volatility regressions,” SFB 649 Economic Risk Berlin, Germany, 2010.
- M. C. Quenez, Méthodes de contrôle stochastique en finance [Thèse de doctorat], Université Pierre et Marie Curie, 1993.
- Ł. Delong, Backward Stochastic Differential Equations With Jumps and Their Actuarial and Financial Applications, EAA, Springer, New York, NY, USA, 2013.
- Y. Su and L. Lin, “Semi-parametric estimation for forward-backward stochastic differential equations,” Communications in Statistics, vol. 38, no. 11, pp. 1759–1775, 2009.
- X. Chen and L. Lin, “Nonparametric estimation for FBSDEs models with applications in finance,” Communications in Statistics, vol. 39, no. 14, pp. 2492–2514, 2010.
- R. Stanton, “A nonparametric model of term structure dynamics and the market price of interest rate risk,” The Journal of Finance, vol. 52, no. 5, pp. 1973–2002, 1997.
- B. Øksendal, Stochastic Differential Equations, Universitext, Springer, New York, NY, USA, 6th edition, 2003.
- M. Rosenblatt, “A central limit theorem and a strong mixing condition,” Proceedings of the National Academy of Sciences of the United States of America, vol. 42, no. 1, pp. 43–47, 1956.
- M. Rosenblatt, “Density estimates and Markov sequencef,” in Selected Works of Murray Rosenblatt, p. 240, Springer, New York, NY, USA, 2011.
- A. N. Kolmogorov and Y. A. Rozanov, “On strongmixing conditions for stationary gaussian processes,” Theory of Probability & Its Applications, vol. 5, no. 2, pp. 204–208, 1960.
- R. C. Bradley and W. Bryc, “Multilinear forms and measures of dependence between random variables,” Journal of Multivariate Analysis, vol. 16, no. 3, pp. 335–367, 1985.
- Z. Lin and C. Lu, Limit Theory for Mixing Dependent Random Variables, vol. 378 of Mathematics and its Applications, Springer, New York, NY, USA, 1996.
- C. N. Morris, “Natural exponential families with quadratic variance functions,” The Annals of Statistics, vol. 10, no. 1, pp. 65–80, 1982.
- G. M. Constantinides, “A theory of the nominal term structure of interest rates,” The Review of Financial Studies, vol. 5, no. 4, pp. 531–552, 1992.
- J. Fan, “A selective overview of nonparametric methods in financial econometrics,” Statistical Science, vol. 20, no. 4, pp. 317–357, 2005.
- J. Fan and C. A. Zhang, “A reexamination of diffusion estimators with applications to financial model validation,” Journal of the American Statistical Association, vol. 98, no. 461, pp. 118–134, 2003.
- K. C. Chan, G. A. Karolyi, F. A. Longstaff, and A. B. Sanders, “An empirical comparison of alternative models of the short-term interest rate,” The Journal of Finance, vol. 47, no. 3, pp. 1209–1227, 1992.
- Y. Aït-Sahalia, “Testing continuous-time models of the spot interest rate,” The Review of Financial Studies, vol. 9, no. 2, pp. 385–426, 1996.
- N. El Karoui, S. Peng, and M. C. Quenez, “Backward stochastic differential equations in finance,” Mathematical Finance, vol. 7, no. 1, pp. 1–71, 1997.
- D. N. Politis and J. P. Romano, “A general resampling scheme for triangular arrays of -mixing random variables with application to the problem of spectral density estimation,” The Annals of Statistics, vol. 20, no. 4, pp. 1985–2007, 1992.
- X. Cui, W. Guo, L. Lin, and L. Zhu, “Covariate-adjusted nonlinear regression,” The Annals of Statistics, vol. 37, no. 4, pp. 1839–1870, 2009.
- M. Peligrad, “Properties of uniform consistency of the kernel estimators of density and of regression functions under dependence assumptions,” Stochastics and Stochastics Reports, vol. 40, no. 3-4, pp. 147–168, 1992.
- T. Y. Kim and D. D. Cox, “Uniform strong consistency of kernel density estimators under dependence,” Statistics & Probability Letters, vol. 26, no. 2, pp. 179–185, 1996.