TY - JOUR
A2 - Dragan, Vasile
AU - Zhang, Qi
PY - 2013
DA - 2013/11/02
TI - Terminal-Dependent Statistical Inference for the Integral Form of FBSDE
SP - 753025
VL - 2013
AB - Backward Stochastic Differential Equation (BSDE) has been well studied and widely applied. The main difference from the Original Stochastic Differential Equation (OSDE) is that the BSDE is designed to depend on a terminal condition, which is a key factor in some financial and ecological circumstances. However, to the best of knowledge, the terminal-dependent statistical inference for such a model has not been explored in the existing literature. This paper is concerned with the statistical inference for the integral form of Forward-Backward Stochastic Differential Equation (FBSDE). The reason why I use its integral form rather than the differential form is that the newly proposed inference procedure inherits the terminal-dependent characteristic. In this paper the FBSDE is first rewritten as a regression version, and then a semiparametric estimation procedure is proposed. Because of the integral form, the newly proposed regression version is more complex than the classical one, and thus the inference methods are somewhat different from those designed for the OSDE. Even so, the statistical properties of the new method are similar to the classical ones. Simulations are conducted to demonstratefinite sample behaviors of the proposed estimators.
SN - 1026-0226
UR - https://doi.org/10.1155/2013/753025
DO - 10.1155/2013/753025
JF - Discrete Dynamics in Nature and Society
PB - Hindawi Publishing Corporation
KW -
ER -