Seminar in applied mathematics and statistics

SPEAKER: Holger Kraft, Goethe University Frankfurt

TITLE: Asset Pricing and Consumption-Portfolio Choice with Recursive Utility and Unspanned Risk

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.  (Joint work with Thomas Seiferling and Frank Thomas Seifred.)