带比例交易成本的投资组合选择

Portfolio selection at proportional transaction costs

介绍了在完备市场下用鞅方法解决最优投资组合的问题.存在交易成本和交易约束的情况下,提出了用条件Delta对冲模型进行期权复制,最小化复制误差,得到最优对冲下的波动率,即调整后的波动率,再将调整后的波动率代替鞅方法下的投资组合波动率,就得到了存在交易成本和交易约束下的最优投资组合.通过Monte Carlo模拟的方法来计算最优投资组合.数值结果显示了交易成本和其他参数对最优投资组合策略的影响,并将其与完备市场下的投资组合进行了比较.

Martingale approach is introduced to solve the problem of optimal portfolio in complete markets. With the consideration of the transaction costs and trading restrictions, a conditional delta hedging model is proposed to replicate the option. By minimizing the absolute replication error, the optimal hedging volatility is yielded, namely the adjusted volatility, and then this adjusted volatility with martingale approach is integrated to achieve the optimal portfolio in presence of transaction costs and trading restrictions. The method relies on Monte Carlo simulation to compute numerically the value of optimal portfolio with proportional transaction costs. Numerical results show that transaction costs, the other parameters effects on the optimal investment policy and the value of the optimal portfolio are compared in complete markets with the one in presence of the transaction costs.