3 research outputs found
Convergence Analysis of Adaptive Critic Based Optimal Control
Adaptive critic based neural networks have been found to be powerful tools in solving various optimal control problems. The adaptive critic approach consists of two neural networks which output the control values and the Lagrangian multipliers associated with optimal control. These networks are trained successively and when the outputs of the two networks are mutually consistent and satisfy the differential constraints, the controller network output produces optimal control. In this paper, we analyze the mechanics of convergence of the network solutions. We establish the necessary conditions for the network solutions to converge and show that the converged solution is optimal
A closed-form estimator for the multivariate GARCH(1,1) model
We provide a closed-form estimator based on the VARMA representation for the
unrestricted multivariate GARCH(1,1). We show that all parameters can be
derived using basic linear algebra tools. We show that the estimator is
consistent and asymptotically normal distributed. Our results allow also to
derive a closed form for the parameters in the context of temporal aggregation
of multivariate GARCH(1,1) by solving the equations as in Hafner [2008]