Finite horizon consumption and portfolio decisions with stochastic hyperbolic discounting

We study finite horizon consumption and portfolio decisions of time-inconsistent individuals by incorporating the stochastic hyperbolic preferences of Harris and Laibson (2013) into the classical model of Merton (1969, 1971) with constant relative risk aversion (CRRA). We obtain closed-form solutions for optimal consumption and portfolio choices for sophisticated individuals with log utility and numerical solutions for those with power utility. Compared to the results of Merton, we find that stochastic hyperbolic discounting increases the consumption rate but has no effect on the share of wealth invested in the risky asset.