Rainer Buckdahn and Naoyuki
Ichihara.
Titre:
"Limit theorem for controlled backward SDEs and homogenization of Hamilton-Jacobi-Bellman equations.
"
Abstract :
We prove a convergence theorem for a family of value functions associated with
stochastic control problems whose cost functions are defined by backward
stochastic differential equations. The limit function is characterized as a
viscosity solution to a fully nonlinear partial differential equations of second
order. The key assumption we use in our approach is shown to be necessary and
sufficient assumption for the homogenizability of the control problem. The
results generalize partially homogenization problems for Hamilton-Jacobi-Bellman
equations treated recently by Alvarez and Bardi by viscosity solution methods.
In contrast to their approach, we use mainly probabilistic arguments, and
discuss a stochastic control interpretation for the limit equation.