Faculty of Economics and Business Administration Publications Database

Optimal consumption and investment with Epstein–Zin recursive utility

Seiferling, Thomas
Seifried, Frank Thomas
Volume: 21
Number: 1
Pages: 187 - 226
Month: January
ISSN-Print: 0949-2984
Link External Source: Online Version
Year: 2017
Keywords: Consumption-portfolio choice; Asset pricing; Stochastic differential utility; Incomplete markets; Fixed point approach; FBSDE

We study continuous-time optimal consumption and investment with Epstein–Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton–Jacobi–Bellman equation by a fixed point argument and makes it possible to compute both the indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.