Abstract
We investigate the joint consumption-saving and portfolio-selection problem under capital risk, assuming sophisticated but time-inconsistent agents. We introduce stochastic hyperbolic preferences as specified in Harris and Laibson (2008) and find closed-form solutions for the classic Merton (1969, 1971) optimal consumption and portfolio selection problem in continuous time. The portfolio rule remains identical to the time-consistent solution with power utility with no borrowing constraints. However, the marginal propensity to consume out of wealth is unambiguously greater than the time-consistent, exponential case.
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