Pith Number

pith:EHAL2UMG

pith:2026:EHAL2UMGAPL7JR7EB6IOI6QH22

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On the Expected Maximum Deficit and the Optimal Allocation of Reserves

Claude Lefevre, Pierre Zuyderhoff

The expected maximum deficit defines coherent risk measures and permits exact analytical optimization of aggregate minimum reserves across business lines.

arxiv:2605.16448 v1 · 2026-05-15 · q-fin.RM · math.PR · q-fin.PM

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Claims

C1strongest claim

Theoretical results established include static coherence and convexity properties, dynamic conditional extensions detailing supermartingale time consistency over a fixed horizon and the evolution of capital requirements across rolling horizons, and exact analytical optimizations of the aggregate minimum reserve.

C2weakest assumption

The continuous-time framework permits formalization of the expected maximum deficit and supports the definition of implicitly bounded risk measures based on minimal capital required to meet prescribed fixed and proportional risk tolerances.

C3one line summary

The paper establishes coherence, convexity, and time-consistency properties for expected-maximum-deficit risk measures and derives exact analytical solutions for optimal aggregate minimum reserves under fixed and proportional tolerances.

References

29 extracted · 29 resolved · 0 Pith anchors

[1] M., and Heath, D 1999

[2] R., Cialenco, I., and Liu, H 2025

[3] Bion-Nadal, J. (2008). Time consistent convex measures of risk.Mathematical Finance, 18(4):683–705 2008

[4] Cheng, Y., and Pai, J. S. (2003). On the nth stop-loss transform order of ruin probability. Insurance: Mathematics and Economics, 32(1):51–60. 31 2003

[5] Cheridito, P., Delbaen, F., and Kupper, M. (2005). Coherent and convex monetary risk measures for unbounded c` adl` ag processes.Finance and Stochastics, 9(3):369–387 2005

Formal links

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Receipt and verification

First computed	2026-05-20T00:02:22.648744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21c0bd518603d7f4c7e40f90e47a07d6906a424d904ffa6bf24e4dcc7daa658c

Aliases

arxiv: 2605.16448 · arxiv_version: 2605.16448v1 · doi: 10.48550/arxiv.2605.16448 · pith_short_12: EHAL2UMGAPL7 · pith_short_16: EHAL2UMGAPL7JR7E · pith_short_8: EHAL2UMG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EHAL2UMGAPL7JR7EB6IOI6QH22 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 21c0bd518603d7f4c7e40f90e47a07d6906a424d904ffa6bf24e4dcc7daa658c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc963c7f1b511ec0543f6ded797ae5b119acb0b1e57f0e059e97350bfb82db60",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.PM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.RM",
    "submitted_at": "2026-05-15T03:04:50Z",
    "title_canon_sha256": "eccd3235152d60fa8fe8dad7320495be847a540d0e621f58f272bff6931b6121"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16448",
    "kind": "arxiv",
    "version": 1
  }
}