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.

Keywords: Merton's model, Knightian uncertainty, Model contamination, Model misspecification, Robust decision-making

JEL Classifications: C60, C61, G11

Accepted Paper Series