Dynamic Asset Allocation and Consumption under Time-inconsistent Preferences

Experimental evidence suggests that time preferences play an important role in intertemporal decisions. In a stochastic economy with two fundamental sources of risk, using the martingale method, I present closed-form solutions for optimal consumption and investment for a CRRA agent under any time preference. I introduce a generic discount function, with exponential and quasi-hyperbolic discounting as well-known special forms of time-consistent and time-inconsistent behaviour, respectively. Time-inconsistent preferences increase the consumption rate due to a desire for immediate gratification. There is no effect on the proportions of wealth invested in each asset, but invested monetary amounts are lower for time-inconsistent individuals. I identify similarities and differences with a deterministic economy. Special attention is devoted to a pension context.