Stochastic maximum principle for stochastic recursive optimal control problem under volatility ambiguity

TL;DR

This paper develops a stochastic maximum principle for recursive optimal control problems under volatility ambiguity, using linearization and weak convergence methods, applicable to financial models with uncertain volatility.

Contribution

It introduces a novel maximum principle for control problems driven by G-Brownian motion, addressing volatility ambiguity with a new analytical approach.

Findings

Establishes a maximum principle for G-Brownian motion driven control problems.

Provides a framework for economic and financial optimization under volatility uncertainty.

Demonstrates the applicability of the approach to problems with recursive cost functionals.

Abstract

We study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Some of the economic and financial optimization problems with volatility ambiguity can be formulated as such problems. Different from the classical variational approach, we establish the maximum principle by the linearization and weak convergence methods.