Scaling limit for solutions of BSDEs driven by population dynamics

Paul Jusselin (1) , Thibaut Mastrolia (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

Going from a scaling approach for birth/death processes, we investigate the convergence of solutions to BSDEs 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.

Mots clés: backward stochastic differential equation (BSDE); stability of BSDEs; martingale properties; birth and death processes; population models; stochastic control

Domaines: Probabilités [math.PR]

Paul Jusselin, Thibaut Mastrolia. Scaling limit for solutions of BSDEs driven by population dynamics. 2019. ⟨hal-02343212⟩