Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach
Dynamic portfolio optimization with liquidity cost and market impact: a simulation-and-regression approach
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DOI：
10.1080/14697688.2018.1524155
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发表时间：
2016-10
影响因子：
1.3
通讯作者：
Rongju Zhang;Nicolas Langren'e;Yu Tian;Zili Zhu;F. Klebaner;K. Hamza
中科院分区：
文献类型：
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作者：
Rongju Zhang;Nicolas Langren'e;Yu Tian;Zili Zhu;F. Klebaner;K. Hamza
我们提出了一个模拟和回归的方法来解决一般的交易成本，流动性成本和市场影响的存在下的动态投资组合优化问题。该方法扩展了经典的最小二乘蒙特卡罗算法，引入了转换成本（对应于交易成本和瞬时流动性成本）以及多个内生状态变量（即投资组合价值和受市场永久影响的资产价格）。为了处理内生状态变量，我们采用控制随机化方法来解决投资组合优化问题，并进一步提高了离散控制情况下该技术的数值精度。我们通过求解一个现实的现金和股票组合与幂律流动性模型验证我们修改的数值方法。我们确定的确定性等价损失忽略流动性的影响，并说明我们的动态优化方法如何保护投资者的资本在非流动性的市场条件下。最后，在不同的流动性条件下，分析了确定性等价收益和最优配置对交易量、股价波动率、初始投资额、风险厌恶水平和投资期限的敏感性。
We present a simulation-and-regression method for solving dynamic portfolio optimization problems in the presence of general transaction costs, liquidity costs and market impact. This method extends the classical least squares Monte Carlo algorithm to incorporate switching costs, corresponding to transaction costs and transient liquidity costs, as well as multiple endogenous state variables, namely the portfolio value and the asset prices subject to permanent market impact. To handle endogenous state variables, we adapt a control randomization approach to portfolio optimization problems and further improve the numerical accuracy of this technique for the case of discrete controls. We validate our modified numerical method by solving a realistic cash-and-stock portfolio with a power-law liquidity model. We identify the certainty equivalent losses associated with ignoring liquidity effects, and illustrate how our dynamic optimization method protects the investor's capital under illiquid market conditions. Lastly, we analyze, under different liquidity conditions, the sensitivities of certainty equivalent returns and optimal allocations with respect to trading volume, stock price volatility, initial investment amount, risk aversion level and investment horizon.