Better than pre-commitment mean-variance portfolio allocation strategies: A semi-self-financing Hamilton-Jacobi-Bellman equation approach

6 7 Expanded Version 8 We generalize the idea of semi-self-financing strategies, originally discussed in Ehrbar, Journal of 9 Economic Theory (1990), and later formalized in Cui et al, Mathematical Finance 22 (2012), for 10 the pre-commitment mean-variance (MV) optimal portfolio allocation problem. The proposed 11 semi-self-financing strategies are built upon a numerical solution framework for Hamilton-Jacobi12 Bellman equations, and can be readily employed in a very general setting, namely continuous 13 or discrete re-balancing, jump-diffusions with finite activity, and realistic portfolio constraints. 14 We show that if the portfolio wealth exceeds a threshold, an MV optimal strategy is to with15 draw cash. These semi-self-financing strategies are generally non-unique. Numerical results 16 confirming the superiority of the efficient frontiers produced by the strategies with positive cash 17 withdrawals are presented. Tests based on estimation of parameters from historical time series 18 show that the semi-self-financing strategy is robust to estimation ambiguities. 19