Optimal consumption and investment in incomplete markets with general constraints

TL;DR

This paper provides explicit solutions for optimal consumption and investment in incomplete markets with general constraints, using martingale methods and BSDEs with quadratic growth drivers.

Contribution

It introduces a novel approach to solve the problem with non-convex constraints using advanced BSDE techniques, extending previous models.

Findings

Explicit solutions for exponential, logarithmic, and power utilities.

Applicable to incomplete markets with general stochastic constraints.

Utilizes recent advances in BSDE theory for quadratic growth drivers.

Abstract

We study an optimal consumption and investment problem in a possibly incomplete market with general, not necessarily convex, stochastic constraints. We give explicit solutions for investors with exponential, logarithmic and power utility. Our approach is based on martingale methods which rely on recent results on the existence and uniqueness of solutions to BSDEs with drivers of quadratic growth.