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Nonparametric estimation for FBSDEs models with applications in finance. (English) Zbl 1201.62041
Summary: As a continuous-time model, forward-backward stochastic differential equations (in short FBSDEs) have been successfully applied in mathematical finance, e.g., European option pricing for either a small or a large investor in a Markovian market. However, the correct FBSDEs model for a specific topic can neither be provided automatically by financial markets nor derived from the theory of mathematical finance. In this article, a nonparametric FBSDEs model is adopted for its flexibility and robustness, and the estimators of the functional coefficients of the FBSDEs model are obtained. The asymptotic properties of the estimators are also discussed. A simulation is performed to test the feasibility of our method.
MSC:
62G05Nonparametric estimation
62G08Nonparametric regression
62E20Asymptotic distribution theory in statistics
62G20Nonparametric asymptotic efficiency
62P05Applications of statistics to actuarial sciences and financial mathematics
62M05Markov processes: estimation
60H10Stochastic ordinary differential equations
65C60Computational problems in statistics