论文标题
Markowitz投资组合选择用于多元仿射和二次Volterra模型
Markowitz portfolio selection for multivariate affine and quadratic Volterra models
论文作者
论文摘要
本文涉及在粗糙协方差矩阵下使用多个资产的投资组合选择。我们研究了多元仿射和二次伏尔泰拉模型的连续时间Markowitz均值变化问题。 在这个具有无限随机系数的不完整的非马克维亚和非 - 障碍市场框架中，最佳投资组合策略是通过Riccati向后的随机微分方程（BSDE）表示的。 对于仿射伏特拉模型，我们根据多维riccati-volterra方程来得出该BSDE的明确解决方案。该框架包括多元粗糙的Heston模型，并扩展了\ cite {Han2019mean}的结果。在二次情况下，我们获得了Riccati BSDE的新分析公式，并与无限尺寸riccati方程建立了它们的联系。这涵盖了粗糙的Stein-Stein和Wishart类型的协方差模型。 在二维粗糙的Stein-Stein模型上的数值结果说明了粗糙波动和随机相关性对最佳Markowitz策略的影响。特别是对于正相关的资产，我们发现模型中的最佳策略是“购买粗糙卖出”。
This paper concerns portfolio selection with multiple assets under rough covariance matrix. We investigate the continuous-time Markowitz mean-variance problem for a multivariate class of affine and quadratic Volterra models. In this incomplete non-Markovian and non-semimartingale market framework with unbounded random coefficients, the optimal portfolio strategy is expressed by means of a Riccati backward stochastic differential equation (BSDE). In the case of affine Volterra models, we derive explicit solutions to this BSDE in terms of multi-dimensional Riccati-Volterra equations. This framework includes multivariate rough Heston models and extends the results of \cite{han2019mean}. In the quadratic case, we obtain new analytic formulae for the the Riccati BSDE and we establish their link with infinite dimensional Riccati equations. This covers rough Stein-Stein and Wishart type covariance models. Numerical results on a two dimensional rough Stein-Stein model illustrate the impact of rough volatilities and stochastic correlations on the optimal Markowitz strategy. In particular for positively correlated assets, we find that the optimal strategy in our model is a `buy rough sell smooth' one.
