We explore a novel solution method, namely that of penalized dual martingales. This method solves the dual problem, which is posed as finding a martingale acting as Lagrange multiplier of the non-anticipativity constraint of the primal control problem. Any feasible solution of the dual problem yields an upper bound on the objective value of the primal (maximization) problem. The infinite-dimensional dual problem is condensed into a finite-dimensional problem by restricting the set of martingales to a finite-dimensional subspace and solved by Monte-Carlo simulations. In order for the method to converge to an almost surely optimal martingale, i.e., for which the upper bound of the objective value has vanishing variance (see [SZH13]), a penalty term is added to the objective function.