Optimal consumption and investment with Epstein–Zin recursive utility
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- 作者：Holger Kraft ; Thomas Seiferling ; Frank Thomas Seifried
- 关键词：Consumption ; portfolio choice ; Asset pricing ; Stochastic differential utility ; Incomplete markets ; Fixed point approach ; FBSDE
- 刊名：Finance and Stochastics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：21
- 期：1
- 页码：187-226
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Quantitative Finance; Finance, general; Statistics for Business/Economics/Mathematical Finance/Insurance; Economic Theory/Quantitative Economics/Mathematical Methods; Probability Theory and Stochastic
- 出版者：Springer Berlin Heidelberg
- ISSN：1432-1122
- 卷排序：21
文摘
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.