Optimal Consumption and Investment Decisions Under Time-Varying Risk Attitudes

Abstract

When finding the optimal consumption and investment decision rules of an individual, accounting for a change in the risk aversion over the life cycle is an important aspect. Different methods are suggested in the literature. This paper combines the two approaches of including a habit level (see e.g. Constantinides, 1990) and a coefficient of time-varying risk aversion (see e.g. Steffensen, 2011). The optimal decision rules are derived in a complete market and examined in a numerical analysis.

Our findings show that with a coefficient of time-varying risk aversion, the shape of the decision rules, rather than just their magnitude, depends on the initial wealth of the individual. Furthermore, a time-increasing risk aversion and sufficiently large habit formation lead to a hump-shaped consumption pattern and a decreasing investment into the risky asset, as observed in the literature.

Keywords: Optimal consumption and investment, habit formation, time-varying risk aversion

JEL Classification: D91, G11