Optimal Consumption and Investment with Epstein-Zin Recursive Utility

Finance and Stochastics, Vol. 21, Issue 1, pp. 187-226
Holger Kraft,
Thomas Seiferling,
Frank Thomas Seifried
Reseach Area:
Financial Markets

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.

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