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...

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Bibliographic Details
Published in:Finance and stochastics Vol. 21; no. 1; pp. 187 - 226
Main Authors: Kraft, Holger, Seiferling, Thomas, Seifried, Frank Thomas
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2017
Springer Nature B.V
Subjects:
Consumption
Differential equations
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Investments
Management
Mathematical models
Mathematics
Mathematics and Statistics
Numerical analysis
Partial differential equations
Probability Theory and Stochastic Processes
Quantitative Finance
Recursion
Statistics for Business
Studies
Volatility
D52
Fixed point approach
FBSDE
C68
G11
G12
Stochastic differential utility
93E20
91G10
Consumption-portfolio choice
Incomplete markets
91B25
D91
Asset pricing
C61
ISSN:0949-2984, 1432-1122
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0949-2984
1432-1122
DOI:10.1007/s00780-016-0316-0