Abstract
Our aim is to provide a (nonlinear) Feynman-Kac type representation for viscosity solutions to fully nonlinear partial differential equations of Hamilton-Jacobi-Bellman (HJB) type.
The unique viscosity solution to such an equation turns out to be the value function of a suitable stochastic optimal control problem.
By nonlinear Feynman-Kac representation we mean a probabilistic representation formula, obtained in terms of a Backward Stochastic Differential Equation (BSDE).
In the fully nonlinear case, such representation has been obtained only recently by means of the so called control randomization method.
The nonlinear Feynman-Kac formula is particularly important since it can be used, for instance, to derive a probabilistic numerical scheme for the solution to the HJB equation, whence for the value
function of the stochastic optimal control problem.
In the talk we will present this new methodology and we will apply it to a particular class of HJB equations, which are associated to control problems of non-diffusive Markov processes.
The corresponding value function, that is the unique viscosity solution to a first order integro-differential HJB equation, is then related to a BSDE driven by a random measure, whose solution
has a sign constraint on one of its components.
