Optimal Consumption and Investment with Epstein-Zin Recursive Utility

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 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.

Keywords: consumption-portfolio choice, asset pricing, stochastic differential utility, incomplete markets, fixed point approach, FBSDE

JEL Classification: G11, G12, D52, D91, C61, C68

Suggested Citation: Suggested Citation

Kraft, Holger and Seiferling, Thomas and Seifried, Frank Thomas, Optimal Consumption and Investment with Epstein-Zin Recursive Utility (July 4, 2016). SAFE Working Paper No. 52, Available at SSRN: https://ssrn.com/abstract=2444747 or http://dx.doi.org/10.2139/ssrn.2444747