A0655
Title: Efficient drift parameter estimation for ergodic solutions of backward SDEs
Authors: Teppei Ogihara - University of Tokyo (Japan) [presenting]
Mitja Stadje - Ulm University (Germany)
Abstract: Efficient drift parameter estimation is explored for ergodic solutions of backward stochastic differential equations (BSDEs). Traditional methods for estimating parameters in stochastic differential equations (SDEs) often assume known parametric forms for the diffusion coefficient. However, the diffusion coefficient is not parametrized nor observed when the process is BSDE. A maximum likelihood type estimation method is proposed that leverages discrete observations of the BSDE to estimate the drift parameter in the presence of an unknown diffusion coefficient. The approach involves constructing quasi-log-likelihood functions using discrete-time observations and employing ergodic properties of the underlying processes. Under appropriate smoothness and non-degeneracy conditions, the maximum likelihood estimators (MLEs) for the drift parameter are demonstrated to achieve asymptotic normality, ensuring reliable and consistent parameter estimation as the sample size increases. Numerical experiments are conducted to validate the theoretical results and to illustrate the practical performance of the proposed estimators.
