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Optimal consumption and investment with Epstein–Zin recursive utility

Holger Kraft (), Thomas Seiferling () and Frank Thomas Seifried ()
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Holger Kraft: Goethe University
Thomas Seiferling: University of Kaiserslautern
Frank Thomas Seifried: University of Trier

Finance and Stochastics, 2017, vol. 21, issue 1, pages 187-226

Abstract: Abstract 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.

Keywords: Consumption-portfolio choice; Asset pricing; Stochastic differential utility; Incomplete markets; Fixed point approach; FBSDE; 93E20; 91G10; 91B25 (search for similar items in EconPapers)
JEL-codes: G11 G12 D52 D91 C61 C68 (search for similar items in EconPapers)
Date: 2017
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