A note on robustness in Merton's model of intertemporal consumption and portfolio choice

Abstract

The paper presents a robust version of a simple two-assets Merton (1969, Review of Economics and Statistics 51, 247–57) model where the optimal choices and the implied shadow market prices of risk for a representative robust decision maker (RDM) can be easily described. With the exception of the log-utility case, precautionary behaviour is induced in the optimal consumption–investment rules through a substitution of investment in risky assets with both current consumption and riskless saving. For the log-utility case, precautionary behaviour arises only through a substitution between risky and riskless assets. On the financial side, the decomposition of the market price of risk in a standard consumption based component and a further price for model uncertainty risk (which is positively related to the robustness parameter) is independent of the underlying risk aversion parameter.