TL;DR
This paper provides a detailed mathematical foundation of Markowitz geometry, focusing on the intersection theory of ellipsoids and affine subspaces, which underpins the mean-variance portfolio theory in economics.
Contribution
It offers a comprehensive and self-contained treatment of Markowitz geometry, clarifying its mathematical structure and relevance to portfolio optimization.
Findings
Detailed mathematical characterization of ellipsoid and affine subspace intersections.
Solid foundation for the application of Markowitz geometry in economics.
Clarification of classical intersection theory in a modern mathematical context.
Abstract
By Markowitz geometry we mean the intersection theory of ellipsoids and affine subspaces in a real finite-dimensional linear space. In the paper we give a meticulous and self-contained treatment of this arch-classical subject, which lays a solid mathematical groundwork of Markowitz mean-variance theory of efficient portfolios in economics.
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Taxonomy
TopicsRisk and Portfolio Optimization · Stochastic processes and financial applications · Economic theories and models