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**Better than pre-commitment mean-variance portfolio allocation strategies: a semi-self-financing Hamilton-Jacobi-Bellman equation approach.**
*(English)*
Zbl 1348.91250

Summary: We generalize the idea of semi-self-financing strategies, originally discussed in [H. Ehrbar, J. Econ. Theory 50, No. 1, 214–218 (1990; Zbl 0686.90008)], and later formalized in [X. Cui et al., Math. Finance 22, No. 2, 346–378 (2012; Zbl 1278.91131)], for the pre-commitment mean-variance (MV) optimal portfolio allocation problem. The proposed semi-self-financing strategies are built upon a numerical solution framework for Hamilton-Jacobi-Bellman equations, and can be readily employed in a very general setting, namely continuous or discrete re-balancing, jump-diffusions with finite activity, and realistic portfolio constraints. We show that if the portfolio wealth exceeds a threshold, an MV optimal strategy is to withdraw cash. These semi-self-financing strategies are generally non-unique. Numerical results confirming the superiority of the efficient frontiers produced by the strategies with positive cash withdrawals are presented. Tests based on estimation of parameters from historical time series show that the semi-self-financing strategy is robust to estimation ambiguities.

### MSC:

91G10 | Portfolio theory |

35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |

49L20 | Dynamic programming in optimal control and differential games |

60H30 | Applications of stochastic analysis (to PDEs, etc.) |

62P05 | Applications of statistics to actuarial sciences and financial mathematics |

93E20 | Optimal stochastic control |

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\textit{D. M. Dang} and \textit{P. A. Forsyth}, Eur. J. Oper. Res. 250, No. 3, 827--841 (2016; Zbl 1348.91250)

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