publication . Preprint . 2017

Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *

Ismail, Amine; Pham, Huyên;
Open Access English
  • Published: 11 Mar 2017
  • Publisher: HAL CCSD
Abstract
This paper studies a robust continuous-time Markowitz portfolio selection pro\-blem where the model uncertainty carries on the covariance matrix of multiple risky assets. This problem is formulated into a min-max mean-variance problem over a set of non-dominated probability measures that is solved by a McKean-Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman-Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies and illustrate our results in the case of uncertain volatilities and ambiguous correlation between two risky assets...
Subjects
arxiv: Mathematics::Optimization and Control
free text keywords: Continuous-time Markowitz problem, Mathematics - Optimization and Control, Quantitative Finance - Portfolio Management, Wasserstein space, covariance matrix uncertainty, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Probability, ambiguous correlation, dynamic programming, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], McKean-Vlasov
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publication . Preprint . 2017

Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *

Ismail, Amine; Pham, Huyên;