Efficient frontiers for portfolios under SSD and law-invariant risk measures with hyperbolic return distributions

[2202.02488] Efficient frontiers for portfolios under SSD and law-invariant risk measures with hyperbolic return distributions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantitative Finance > Mathematical Finance arXiv:2202.02488 (q-fin) [Submitted on 5 Feb 2022 ( v1 ), last revised 16 Aug 2026 (this version, v11)] Title: Efficient frontiers for portfolios under SSD and law-invariant risk measures with hyperbolic return distributions Authors: Hasanjan Sayit View a PDF of the paper titled Efficient frontiers for portfolios under SSD and law-invariant risk measures with hyperbolic return distributions, by Hasanjan Sayit View PDF HTML (experimental) Abstract: In the classical Markowitz mean variance framework, risk is measured by variance, and the portfolios on the efficient frontier can be derived in closed form using standard optimization methods. For broader mean risk formulations, however, obtaining closed form optimal portfolios is typically difficult. In this work, we derive explicit expressions for frontier portfolios corresponding to arbitrary law-invariant convex risk measures, assuming that the return vector follows a normal mean variance mixture distribution. Our approach first establishes stochastic dominance relations within the family of normal mean variance mixture models, and then leverages these relations to derive closed-form representations of frontier portfolios. The central finding demonstrates that when asset returns are described by a normal mean variance mixture models the associated mean risk efficient frontier can be obtained by solving a Markowitz mean variance problem for a suitably transformed return vector. The paper also extends the CAPM framework to the context of a normal mean variance mixture distribution. Comments: 30pages Subjects: Mathematical Finance (q-fin.MF) MSC classes: 91-XX Cite as: arXiv:2202.02488 [q-fin.MF] (or arXiv:2202.02488v11 [q-fin.MF] for this version) https://doi.org/10.48550/arXiv.2202.02488 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hasanjan Sayit [ view email ] [v1] Sat, 5 Feb 2022 04:39:54 UTC (29 KB) [v2] Wed, 24 Aug 2022 13:26:15 UTC (36 KB) [v3] Thu, 25 Aug 2022 01:57:37 UTC (36 KB) [v4] Sun, 28 May 2023 02:58:08 UTC (48 KB) [v5] Sun, 25 Jun 2023 01:47:57 UTC (53 KB) [v6] Wed, 12 Jul 2023 13:37:56 UTC (1 KB) (withdrawn) [v7] Mon, 9 Dec 2024 07:00:11 UTC (49 KB) [v8] Sun, 19 Jan 2025 05:59:54 UTC (50 KB) [v9] Thu, 5 Mar 2026 02:07:35 UTC (72 KB) [v10] Mon, 16 Mar 2026 03:01:46 UTC (73 KB) [v11] Sun, 16 Aug 2026 01:59:19 UTC (76 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient frontiers for portfolios under SSD and law-invariant risk measures with hyperbolic return distributions, by Hasanjan Sayit View PDF HTML (experimental) TeX Source view license Current browse context: q-fin.MF < prev | next > new | recent | 2022-02 Change to browse by: q-fin References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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