Maximization of recursive utilities under convex portfolio constraints

TL;DR

This paper addresses the problem of maximizing recursive utilities with convex portfolio constraints, establishing existence, uniqueness, and characterizing optimal strategies using BSDEs and duality methods.

Contribution

It introduces a novel approach to solve robust maximization of recursive utilities under convex constraints via quadratic BSDEs and duality, providing theoretical guarantees.

Findings

Existence and uniqueness of optimal strategies proven.

Characterization of optimal control through duality and maximum principle.

Application of quadratic BSDEs to portfolio optimization under constraints.

Abstract

We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the optimal control by using the duality method and deriving a dynamic maximum principle.