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We propose a new probabilistic numerical scheme for fully nonlinear equationof Hamilton-Jacobi-Bellman (HJB) type associated to stochastic control problem,which is based on the Feynman-Kac representation in [12] by means of controlrandomization and backward stochastic differential equation with nonpositivejumps. We study a discrete time approximation for the minimal solution to thisclass of BSDE when the time step goes to zero, which provides both anapproximation for the value function and for an optimal control in feedbackform. We obtained a convergence rate without any ellipticity condition on thecontrolled diffusion coefficient. Explicit implementable scheme based onMonte-Carlo simulations and empirical regressions, associated error analysis,and numerical experiments are performed in the companion paper [13].

Discrete time approximation of fully nonlinear HJB equations via BSDEs with nonpositive jumps