CONTINUOUS‐TIME MEAN‐VARIANCE PORTFOLIO SELECTION WITH BANKRUPTCY PROHIBITION
CONTINUOUS‐TIME MEAN‐VARIANCE PORTFOLIO SELECTION WITH BANKRUPTCY PROHIBITION
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DOI：
10.1111/j.0960-1627.2005.00218.x
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发表时间：
2005-03
影响因子：
1.6
通讯作者：
T. Bielecki;Hanqing Jin;S. Pliska;X. Zhou
中科院分区：
文献类型：
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作者：
T. Bielecki;Hanqing Jin;S. Pliska;X. Zhou
研究了一个连续时间均值-方差投资组合问题，其中所有的市场系数都是随机的，并且在任何可接受的交易策略下，财富过程在任何时刻都不允许小于零。正在考虑的交易策略是根据配置在个别股票中的美元数量来定义的，而不是财富的比例。使用分解方法完全解决了这个问题。具体地说，建立了(约束)方差最小化问题，并对其可行性进行了刻画。然后，在求解两个拉格朗日乘子的方程组后，将方差最小化的投资组合导出为若干未定权益的复制投资组合，并得到了方差最小化的前沿。最后，在证明了期望最终财富在这一部分上的最小方差的单调性并找到所有有效投资组合后，将有效前沿识别为方差最小化前沿的适当部分。在市场系数为确定性的特殊情况下，将有效投资组合显式表示为当期财富的反馈，并用参数方程表示有效前沿。我们的结果表明，对于均值-方差投资者来说，有效的策略是简单地购买欧式看跌期权，该看跌期权是根据他或她的风险偏好从特定的期权类别中选择的。
A continuous‐time mean‐variance portfolio selection problem is studied where all the market coefficients are random and the wealth process under any admissible trading strategy is not allowed to be below zero at any time. The trading strategy under consideration is defined in terms of the dollar amounts, rather than the proportions of wealth, allocated in individual stocks. The problem is completely solved using a decomposition approach. Specifically, a (constrained) variance minimizing problem is formulated and its feasibility is characterized. Then, after a system of equations for two Lagrange multipliers is solved, variance minimizing portfolios are derived as the replicating portfolios of some contingent claims, and the variance minimizing frontier is obtained. Finally, the efficient frontier is identified as an appropriate portion of the variance minimizing frontier after the monotonicity of the minimum variance on the expected terminal wealth over this portion is proved and all the efficient portfolios are found. In the special case where the market coefficients are deterministic, efficient portfolios are explicitly expressed as feedback of the current wealth, and the efficient frontier is represented by parameterized equations. Our results indicate that the efficient policy for a mean‐variance investor is simply to purchase a European put option that is chosen, according to his or her risk preferences, from a particular class of options.