Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities
Portfolio Optimization with Ambiguous Correlation and Stochastic Volatilities
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DOI：
10.2139/ssrn.2479796
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发表时间：
2014-08
期刊：
影响因子：
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通讯作者：
J. Fouque;Chi Seng Pun;H. Y. Wong
中科院分区：
文献类型：
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作者：
J. Fouque;Chi Seng Pun;H. Y. Wong
在连续时间经济中，我们研究无风险资产和两种风险资产之间的资产配置问题，并且两种风险资产之间的相关性不明确。对不确定相关性具有鲁棒性的投资组合选择被公式化为关于可能的相关性选择的最坏情况下的效用最大化问题。因此，它变成了一个极大极小问题。我们使用 G-布朗运动理论解决了 Black-Scholes 模型下具有模糊相关性的风险资产的问题。然后，我们将问题扩展到风险资产的随机波动率模型，风险资产回报之间的相关性不明确。当随机波动快速均值回归时，为一般类效用函数（包括 CRRA 和 CARA 效用）导出渐近封闭式解。我们提出了一种实用的交易策略，通过模糊相关性将风险资产的期权隐含波动率表面的信息结合起来。
In a continuous-time economy, we investigate the asset allocation problem among a risk-free asset and two risky assets with an ambiguous correlation between the two risky assets. The portfolio selection that is robust to the uncertain correlation is formulated as the utility maximization problem over the worst-case scenario with respect to the possible choice of correlation. Thus, it becomes a maximin problem. We solve the problem under the Black-Scholes model for risky assets with an ambiguous correlation using the theory of G-Brownian motions. We then extend the problem to stochastic volatility models for risky assets with an ambiguous correlation between risky asset returns. An asymptotic closed-form solution is derived for a general class of utility functions, including CRRA and CARA utilities, when stochastic volatilities are fast mean-reverting. We propose a practical trading strategy that combines information from the option implied volatility surfaces of risky assets through the ambiguous correlation.