Singular recursive utility

TL;DR

This paper introduces singular recursive utility, explores the associated singular BSDEs, establishes existence and uniqueness conditions, and applies the theory to optimal consumption problems involving Skorohod reflection.

Contribution

It is the first to study singular recursive utility and its related singular BSDEs, providing new theoretical insights and practical applications.

Findings

Established existence and uniqueness of solutions for singular BSDEs.

Derived maximum principles for optimizing singular recursive utility.

Connected the optimal consumption problem to Skorohod reflection solutions.

Abstract

We introduce the concept of singular recursive utility. This leads to a kind of singular BSDE which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular recursive utility. We derive sufficient and necessary maximum principles for this problem, and connect it to the Skorohod reflection problem. Finally, we apply our results to a specific cash flow. In this case, we find that the optimal consumption rate is given by the solution to the corresponding Skorohod reflection problem.