Scaling limit for stochastic control problems in population dynamics

TL;DR

This paper studies how solutions to non-Markovian stochastic control problems in population dynamics behave under scaling limits, showing convergence of optimal controls and values as models approach continuous population models.

Contribution

It introduces a novel approach to analyze the convergence of solutions to BSDEs driven by converging martingales in population control problems.

Findings

Solutions to BSDEs converge as models approach continuous limits

Optimal controls and values also converge under the scaling

Provides a framework for analyzing non-Markovian population control models

Abstract

Going from a scaling approach for birth/death processes, we investigate the scaling limit of solutions to non-Markovian stochastic control problems by studying the convergence of solutions to BSDEs driven a sequence of converging martingales. In particular we manage to describe how the values and optimal controls of control problems converge when the models converge towards a continuous population model.