Robust Consumption and Portfolio Rules When Asset Returns Are Predictable

In his seminal contribution, Merton (1971) solved for the dynamic asset allocation of an expected utility maximizer in a continuous time setting and with an infinite horizon. He showed that when the agent derives utility from intermediate consumption, a closed form solution to the consumption/investment problem exists if the economy is affected by a state variable following a mean reverting process and perfectly positively correlated with the traded risky asset. Wachter (2002) showed that a closed form solution exists under finite horizon when the markets are still complete, that is when there is a perfect negative correlation between the traded risky asset and the state variable. In incomplete markets, a closed form solution is known to exist only when the agent derives utility solely from terminal wealth. Kim and Omberg (1996) consider a setting where a state variable following a mean reverting process is imperfectly correlated to the traded risky asset while the agent has utility only from terminal wealth. In this setting, they showed that a closed form solution exists. Recently, Liu (2007) extended the previous findings to the case where asset returns are quadratic in mean reverting state variables. He obtained explicit solutions in complete markets with intermediate consumption and in incomplete markets with only terminal wealth.