Mean–variance optimization of terminal wealth and consumption

Abstract: We study a portfolio optimization problem for an investor with mean–variance (MV) preferences on terminal wealth and the level of consumption. Our consumption addition differs from other attempts in the literature, allowing for a more flexible treatment. We introduce admissible optimal and admissible efficient solutions to capture the consumption dimension. In a fair comparison to expected utility (EUT), we report a superior performance of our solution. This confirms the pitfall of MV investors using EUT solutions.