Title: Probabilistic interpretation of HJB equations by the representation theorem for generators of BSDEs,
Abstract: The purpose of this note is to propose a new approach for the probabilistic
interpretation of Hamilton-Jacobi-Bellman equations associated with stochastic
recursive optimal control problems, utilizing the representation theorem for
generators of backward stochastic differential equations. The key idea of our
approach for proving this interpretation consists of transmitting the signs
between the solution and generator via the identity given by representation
theorem. Compared with existing methods, our approach seems to be more
applicable for general settings. This can also be regarded as a new application
of such representation theorem.