Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2407.16878

On the Separability of Vector-Valued Risk Measures

Çağın Ararat·Zachary Feinstein
View original source ↗Read source document ↗Export metadata ↓

Abstract

Risk measures for random vectors have been considered in multi-asset markets with transaction costs and financial networks in the literature. While the theory of set-valued risk measures provide an axiomatic framework for assigning to a random vector its set of all capital requirements or allocation vectors, the actual decision-making process requires an additional rule to select from this set. In this paper, we define vector-valued risk measures by an analogous list of axioms and show that, in the convex and lower semicontinuous case, such functionals always ignore the dependence structures of the input random vectors. We also show that set-valued risk measures do not have this issue as long as they do not reduce to a vector-valued functional. Finally, we demonstrate that our results also generalize to the conditional setting. These results imply that convex vector-valued risk measures are not suitable for defining capital allocation rules for a wide range of financial applications including systemic risk measures.

Explore related subjects

q-fin.RM

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Çağın Ararat, Zachary Feinstein. 2024-07-23. On the Separability of Vector-Valued Risk Measures. https://arxiv.org/abs/2407.16878

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Simplifying Cyber Cat(astrophe)s with Cyber Kittens: Power Law Plausibility for Cyber Insurance Risks

Cyber insurance requires accurate modeling of worst-case catastrophic (cat) events, but the field lacks robust quantitative approaches for estimating upper-bound losses. Building on a recent dataset of 24 cyber cat events over 30 years, this work tests whether cyber economic losses follow a power law distribution. We analyze "cyber kittens" - sub-1B USD events distinguished from cat events (1B+ USD) only by magnitude - extracted via LLM from cyber insurance claims data (2020-2024). Using victim count (weighted by claim year) as a proxy for economic loss, we link kitten-sized events to known cat events to estimate losses. The kitten distribution proved consistent with the cat dataset, and power laws were statistically plausible: each order-of-magnitude increase in event size corresponds to a 5-7x drop in probability. Extrapolating, an event 100x the largest 2020-2024 cat event is expected roughly every 206 years, translating to 100-250B USD in losses - catastrophic, but not extraordinary relative to other insurance lines.

q-fin.RM↗
arXiv2026

Identifiability of Contagion Components amid Environmental Fluctuations in Aggregated Default Counts

Can contagion components be identified in aggregated default counts when default probabilities fluctuate with the economic environment? We study this question as an identifiability problem for coarse-grained default-count distributions. We adopt a binomial mixture with a Probit--Normal default probability as a parsimonious null model for environmental fluctuations and test whether contagion provides additional identifiable structure. Against this null, we consider two contagion mechanisms: cumulative contagion in the Davis--Lo model and threshold-type contagion in the Torri model. The Davis--Lo extension substantially improves the likelihood and information criteria for the ALL and speculative-grade classes, whereas the Torri component is largely absorbed by environmental heterogeneity; evidence is weaker for investment-grade defaults. As a robustness test, we replace the Gaussian environmental distribution by a two-component Gaussian mixture, and the Davis--Lo advantage persists for ALL and speculative-grade defaults. These results indicate that cumulative-contagion signatures remain distinguishable from the environmental null models considered here in the ALL and speculative-grade classes, even under annual aggregation.

q-fin.RM↗
arXiv2026

A Certified Higher Order Quantum Framework for CSA and Margin-Aware Collateral Optimization

Collateral allocation for uncleared derivatives is a legally constrained and operationally discrete optimization problem. Institutions must satisfy margin requirements while respecting CSA eligibility rules, valuation percentages, rounding, transfer thresholds, concentration limits, custody conditions, inventory, and VM, IM, or IA side constraints. This manuscript develops CR-HO-QAOA, a certified higher-order quantum candidate-generation framework for margin- and CSA-aware collateral allocation. The framework is adapter-first: official SIMM, proxy SIMM, legacy IA, VM-only, RQV, or hybrid margin sources are normalized into a common MarginRequirement, so the optimizer does not calculate or replace official SIMM. Given the requirement, CSA terms, and inventory, the optimizer builds a bounded active neighborhood of pledge, recall, substitution, batch, and slack actions. These actions define a higher-order binary model whose hyperedges capture concentration pressure, custody batches, substitution tickets, chunky lots, liquidity effects, overshoot, and side-specific requirements. The quantum layer maps hyperedges into a Pauli-Z cost Hamiltonian and uses collateral-specific feasible-subspace mixers to preserve one-hot choices, movement budgets, side assignments, and substitution structure. Candidates are decoded, repaired if needed, evaluated under an eight-term production objective, and certified by a deterministic CP-SAT master solver before any recommendation is reported. Synthetic benchmarks show that higher-order, constraint-preserving candidate generation can improve certified sample quality relative to QUBO-style and generic-mixer baselines, while CP-SAT remains the feasibility and governance arbiter. These results are synthetic workflow-validation evidence only, not evidence of hardware quantum advantage or production bank savings.

q-fin.RM↗