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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.
The utility-maximizing consumption and investment strategy of an individual investor receiving an unspanned labor income stream seems impossible to find in closed form and very dificult to find using numerical solution techniques. We suggest an easy procedure for finding a specific, simple, and admissible consumption and investment strategy, which is near-optimal in the sense that the wealthequivalent loss compared to the unknown optimal strategy is very small. We first explain and implement the strategy in a simple setting with constant interest rates, a single risky asset, and an exogenously given income stream, but we also show that the success of the strategy is robust to changes in parameter values, to the introduction of stochastic interest rates, and to endogenous labor supply decisions.
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.