Optimal Control versus Stochastic Target problems: An Equivalence Result

Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in [17], when-ever the underlying filtered probability space admits a suitable martingale representation property. This provides a unified way of treating these two classes of stochastic con-trol problems. As an illustration, we show, within a jump diffusion framework, how the Hamilton-Jacobi-Bellman equations associated to an optimal control problem in stan-dard form can be easily retrieved from the partial differential equations associated to its stochastic target counterpart