Journal
FINANCE AND STOCHASTICS
Volume 21, Issue 1, Pages 187-226Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00780-016-0316-0
Keywords
Consumption-portfolio choice; Asset pricing; Stochastic differential utility; Incomplete markets; Fixed point approach; FBSDE
Categories
Funding
- Deutsche Forschungsgemeinschaft (DFG)
- Center of Excellence SAFE - State of Hessen initiative for research LOEWE
- Studienstiftung des Deutschen Volkes
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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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