Infinite horizon stochastic differential utility of Epstein-Zin type

In this thesis, we study stochastic differential utility of Epstein–Zin type in a general semimartingale setting. We show that the traditional characterization using the transversality condition identifies an incorrect Epstein–Zin utility in the empirical relevant parameter case. Instead, we present an original characterisation of Epstein–Zin utility in an infinite time horizon and provide sufficient conditions for its existence and uniqueness. In the second half of the thesis, we study an infinite horizon optimal consumption-investment problem in an incomplete, Brownian-driven market for an investor whose preferences are governed by Epstein–Zin utility.