Comparison of optimal portfolios with and without subsistence consumption constraints

Abstract

We present the effects of the subsistence consumption constraints on a portfolio selection problem for an agent who is free to choose when to retire with a constant relative risk aversion (CRRA) utility function. By comparing the previous studies with and without the constraints expressed by the minimum consumption requirement, the changes of a retirement wealth level and the amount of money invested in the risky asset are derived explicitly. As a result, the subsistence constraints always lead to lower retirement wealth level but do not always induce less investment in the risky asset. This implies that even though the agent who has a restriction on consumption retires with lower wealth level, she invests more money near the retirement when her risk aversion lies inside a certain range.