On the Expected Maximum Deficit and the Optimal Allocation of Reserves

[2605.16448] On the Expected Maximum Deficit and the Optimal Allocation of Reserves Skip to main content Search Submit Donate Log in Quantitative Finance > Risk Management arXiv:2605.16448 (q-fin) [Submitted on 15 May 2026 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: On the Expected Maximum Deficit and the Optimal Allocation of Reserves Authors: Claude Lefevre , Pierre Zuyderhoff View PDF HTML (experimental) Abstract: Let $L=(L_s)_{0\le s\le t}$ be a cumulative net-loss process and let $M_t=\sup_{0\le s\le t}L_s$. For a candidate reserve $u$ and a distortion function $g$, define $D_g^{(t)}(u)=\int_u^\infty g(P(M_t>v))d v$. This function measures the tail-weighted residual severity of the largest cumulative loss over the horizon. We derive three monetary risk measures: its value at zero reserve and two measures based on fixed and proportional deficit tolerances. Under a concave distortion, the zero-reserve and proportional-tolerance measures are coherent, while the fixed-tolerance measure is convex. Given a reserve budget distributed among several units, we analyze two allocation criteria: the sum of the units' distorted deficits, which depends only on their marginal distributions, and a distorted expectation of the largest residual unit deficit, which uses their joint distribution. We characterize the optimal allocations and corresponding near-optimal sets. A two-unit exponential benchmark shows that the optimum can be unique and unequal. We then apply both criteria to the Building, Contents and loss-of-Profits components of the public Danish large-fire data. Under the baseline predictive model, both yield interior allocations and localized 0.5\%-optimal regions, while sensitivity analyses illustrate model uncertainty. We also provide Monte Carlo estimators, conditional counterparts and a review-date allocation formulation. Comments: 30 pages, 1 table, 1 figure Subjects: Risk Management (q-fin.RM) ; Probability (math.PR); Portfolio Management (q-fin.PM) MSC classes: 91B30, 60G51 Cite as: arXiv:2605.16448 [q-fin.RM] (or arXiv:2605.16448v3 [q-fin.RM] for this version) https://doi.org/10.48550/arXiv.2605.16448 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pierre Zuyderhoff [ view email ] [v1] Fri, 15 May 2026 03:04:50 UTC (68 KB) [v2] Thu, 13 Aug 2026 02:22:33 UTC (37 KB) [v3] Thu, 27 Aug 2026 07:19:44 UTC (139 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: q-fin.RM < prev | next > new | recent | 2026-05 Change to browse by: math math.PR q-fin q-fin.PM References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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