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Asset pricing and consumption-portfolio choice with recursive utility and unspanned risk

Holger Kraft, Thomas Seiferling and Frank Thomas Seifried

No 52, SAFE Working Paper Series from Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt

Abstract: We study consumption-portfolio and asset pricing frameworks with recursive preferences and unspanned risk. We show that in both cases, portfolio choice and asset pricing, the value function of the investor/representative agent can be characterized by a specific semilinear partial differential equation. To date, the solution to this equation has mostly been approximated by Campbell-Shiller techniques, without addressing general issues of existence and uniqueness. We develop a novel approach that rigorously constructs the solution by a fixed point argument. We prove that under regularity conditions a solution exists and establish a fast and accurate numerical method to solve consumption-portfolio and asset pricing problems with recursive preferences and unspanned risk. Our setting is not restricted to affine asset price dynamics. Numerical examples illustrate our approach.

Keywords: consumption-portfolio choice; asset pricing; stochastic differential utility; incomplete markets; fixed point approach; FBSDE (search for similar items in EconPapers)
JEL-codes: G11 G12 D52 D91 C61 C68 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ore and nep-upt
Date: 2014
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