  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.
