Singular recursive utility

Abstract

We introduce the concept of singular recursive utility. This leads to a kind of singular backward stochastic differential equation (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.

Keywords:

• Singular recursive utility
• singular jump-diffusion processes
• optimal control problem
• stochastic maximum principle
• singular backward stochastic differential equation
• generalized Skorohod reflection problem
• optimal consumption

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was carried out with partial support of CAS – Centre for Advanced Study, at the Norwegian Academy of Science and Letters, within the research program SEFE; Norges Forskningsråd [250768/F20].