Practical volume approximation of high-dimensional convex bodies, applied to modeling portfolio dependencies and financial crises

DOI10.1016/j.comgeo.2022.101916OpenAlexW4286567502WikidataQ114195463 ScholiaQ114195463MaRDI QIDQ2096364

Ioannis Z. Emiris, Vissarion Fisikopoulos, Ludovic Calès, Apostolos Chalkis

Publication date: 16 November 2022

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2022.101916

zbMATH Keywords

samplingconvex bodysimplexempirical financepolytope volume

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Approximation by convex sets (52A27) Portfolio theory (91G10)

Uses Software

• Boost C++ Libraries
• Eigen
• Boost
• ECOS
• PyPortfolioOpt

Cites Work

• Approximating the volume of unions and intersections of high-dimensional geometric objects
• A geometric inequality and the complexity of computing volume
• Dynamic risk exposures in hedge funds
• Hit-and-run mixes fast
• The multidimensional content of the frustum of the simplex
• Content of the frustum of a simplex
• Polytope Volume Computation
• An Active Set Method for Single-Cone Second-Order Cone Programs
• On the Complexity of Computing the Volume of a Polyhedron
• A random polynomial-time algorithm for approximating the volume of convex bodies
• Practical Polytope Volume Approximation
• Geodesic walks in polytopes
• A Cubic Algorithm for Computing Gaussian Volume
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