Scaling Limit for Stochastic Control Problems in Population Dynamics

Going from a scaling approach for birth/death processes, we investigate the convergence of solutions to Backward Stochastic Differential Equations driven a sequence of converging martingales. We apply our results to non-Markovian stochastic control problems for discrete population models. In particular we describe how the values and optimal controls of control problems converge when the models converge towards a continuous population model.