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Contingent Exposure Routing for Financial AI: Outage Risk and the Cost of Indivisible Decisions

Shivam Gupta

arXiv:2610.00239v1cs.LG

TL;DR

Failover can preserve availability while changing which institutions share decision errors, and endpoint counts alone do not characterize financial concentration. The paper models contingent routing with a local response and executable assignment distinctions, then reports risk reductions in synthetic networks and a smaller held-out replay.

  • Problem

    Failover can leave requests available while routing institutions onto a common error, and the operational question is how to assign displaced financial decisions and assess their risk.

    Source: §1 · p. 1

  • Method

    The paper models local price response and compares executable endpoint assignments with fractional allocation under financial exposure and endpoint-error moments.

    Source: §3.1 · p. 3, §3.2 · p. 4

  • Results

    At β=0.4, γ=0, mean reductions are 6.57% for single removals and 10.53% for double removals; held-out replay gives a 3.30% reduction with paired interval 2.07–4.57%.

    Source: §8.1 · p. 9, §8.3 · p. 10

  • Takeaways & Limitations

    The method provides a reproducible way to evaluate contingent routing under declared assumptions, while empirical calibration and independent validation remain necessary before setting operational risk limits.

    Source: §10 · p. 12

    Balance sheets and impact coefficients are synthetic, and the paper does not estimate actual AI adoption or real financial concentration.

    Source: §9 · p. 11

Abstract

from arXiv · show

Model failover restores availability, but changes which financial institutions share decision errors. We formulate outage-contingent routing through a local market-impact response matrix and study expected squared price displacement. A symmetric construction shows that a shared backup can leave an order-one concentration floor as the number of primary endpoints grows, while balanced fallback risk decreases inversely with the surviving endpoint count. For indivisible decisions, we derive the exact second moment of independent randomized routing and an effective-exposure granularity that determines its gap from fractional allocation. Conditional-expectation rounding gives a finite-agent bound without coupled quotas; a separate swap procedure preserves endpoint counts and is assessed against dual lower bounds. Across 60 synthetic portfolio networks and 11,340 scenario evaluations, the latter reduces risk by 6.57% and 10.53% for single and double endpoint removals at the central feedback setting with independent errors. A replay of 1,024 recorded API responses on constructed rebalancing tasks gives a smaller held-out reduction of 3.30% (paired bootstrap interval 2.07--4.57%). Strongly aligned errors, inferior endpoints, and indivisibility limit diversification. The contribution is an auditable routing stress test and implementation analysis, not an estimate of real-market crash probabilities.

1 Introduction

Failover can preserve availability while changing which institutions share decision errors, so request success alone may miss financial exposure concentration. The paper frames routing as an operational assignment problem and distinguishes financial exposure from request counts and indivisible decisions from fractional allocation.

1 Introduction

  • The operational question is which surviving endpoint should receive each displaced financial decision and what risk its executable assignment creates.Institutions may use different endpoints for a common input, then converge on the same backup during an outage.Source: §1 · p. 1
  • Financial exposure propagated through market impact, not request count, is the relevant load, and randomly selecting one endpoint is not equivalent to splitting a decision.Independent endpoint selection introduces assignment variance, so a portfolio-style fractional relaxation can understate executed-policy risk.Source: §1 · p. 1
  • With eight equally weighted primaries and four removals, the illustration contrasts exposure concentrated at one common backup with balanced redistribution.Endpoint labels carry no quality ranking, and the figure concerns financial exposure rather than inference throughput.Source: Figure 1 · p. 2
  • Contingent Exposure Routing combines scenario-specific eligibility, a financial response matrix, and endpoint-error second moments.Its contributions include an outage concentration construction, exact finite-population correction, effective-exposure granularity, and an executable routing procedure.Source: §1 · p. 2

2 Related work

Prior work covers financial propagation, AI-related concentration, model routing, and discrete optimization. This paper positions its contribution at their intersection: routing decisions evaluated through interacting institutional financial exposures.

2 Related work

  • Financial propagation studies motivate the response matrix, but this paper uses a local linear construction rather than reproducing complete stress tests or their empirical calibration.The discussion cites balance-sheet and common-exposure vulnerability and systemic stress testing with liquidity-weighted overlaps and nonlinear deleveraging.Source: §2 · p. 2
  • Work on collective algorithmic consequences and operational concentration motivates studying assignment after endpoint removal, while cyber propagation and endogenous adoption remain outside scope.The paper studies the routing intervention rather than incident frequencies, strategic equilibrium, or financial contagion from vendor compromise.Source: §2 · p. 2
  • Existing model-routing work addresses cost-quality routing [11], misrouting control [6], and joint assignment and resource constraints [9], whereas this objective couples errors through financial exposures.Individual response quality and model-call counts do not determine the resulting objective.Source: §2 · pp. 2–3
  • The paper specializes established rounding, dependent-rounding, and convex-bound ideas,, to financial second moments and distinguishes its guarantee from a quota heuristic.Its scoped literature search does not establish that every component or equivalent formulation is absent from prior work.Source: §2 · p. 3

3 Financial exposure under contingent routing

The framework maps institution-level decision errors through a local financial response and evaluates endpoint assignments using their joint error effects. It distinguishes executable assignments from fractional allocation and fixes the timing and scope of outage evaluation.

3.1 Local price response

  • A local response maps relative decision errors through an exposure matrix and feedback response to price displacement around a fixed operating state.The resulting measure is not automatically a default probability, realized monetary loss, or expected shortfall.Source: §3.1 · p. 3
  • The local response excludes thresholds, insolvency, endogenous liquidity withdrawal, and large-shock saturation, which require a different propagation model.A participation factor multiplying exposure scales all risks by its square; experiments divide it out in normalized units.Source: §3.1 · p. 3

3.2 Errors, outages, and executable assignments

  • Endpoint errors may retain systematic bias and cross-endpoint dependence, and each endpoint error is shared by institutions assigned to it during the decision window.This is a common-input or broadcast-advice model, not a general law for separately prompted agents.Source: §3.2 · p. 3
  • A deterministic assignment gives each institution one eligible endpoint, while a fractional assignment represents actual splitting or linear aggregation rather than independently sampling one endpoint per institution.Equal endpoint quotas imply equal total inference cost only when per-request cost is fixed within each endpoint.Source: §3.2 · pp. 3–4
  • Assignments are selected before evaluated errors are observed, and endpoint-removal experiments hold the error distribution fixed to isolate reassignment.Real outages can alter inputs and error distributions, so the outage-state second moment need not match the normal-state moment.Source: §3.2 · p. 4

4 What primary diversification misses

The symmetric construction shows that a common backup can preserve concentration after endpoint removals, while balanced redistribution lowers the continuous risk benchmark. Growing-outage amplification is limited by common errors and does not describe outage likelihood.

4 What primary diversification misses

  • The common backup carries (r+1)/K exposure while other surviving primaries carry 1/K each; equal survivor loads attain the continuous lower bound.The bound follows because survivor loads sum to one, and balancing requires only displaced mass to move.Source: §4 · p. 4
  • The growing-outage construction is a worst-case family, and with fixed r and K→∞ its common-backup-to-balanced risk ratio tends to one.Growing amplification requires outage size to grow with K.Source: §4 · p. 4
  • A common error component limits relative diversification gains; at γ=1 every feasible routing has identical risk.For scalar unit mass, the common-error term is γ, and routing changes only the other term.Source: §4 · p. 4
  • For r/K→α∈(0,1), common-backup risk tends to α², while balanced risk is asymptotic to [K(1−α)]^-1.Their ratio is asymptotic to α²(1−α)K; these are analytical constructions, not estimates of outage likelihood.Source: §4 · p. 4, Figure 2 · p. 5

5 Indivisible decisions: the missing second moment

Independent randomized routing has an exact second-moment correction relative to fractional allocation. Effective exposure, rather than headcount alone, shapes the resulting granularity gap.

The exact random-routing premium

  • Independent endpoint sampling adds a nonnegative assignment-variance premium to the fractional objective, bounded by λmax(S) times the sum of 1 − ||q_i||² across institutions.The identity applies to independent assignments and allows nonzero mean errors; shared random seeds, coordinated routing, and routing that observes contemporaneous errors change the assignment law.Source: §5 · p. 5

Effective-exposure granularity

  • When pairwise exposure inner products are nonnegative, effective-exposure granularity lies between 1 and n.The lower bound follows from nonnegative pairwise inner products, and the upper bound from Cauchy–Schwarz.Source: §5 · pp. 5–6
  • The routing premium is tied to exposure granularity, so a large headcount need not eliminate a material premium when a few institutions carry large exposures.The supplied definition relates n_eff to aligned exposures and their weights; large institutions can preserve a material premium despite a large headcount.Source: §5 · p. 6
  • With orthogonal exposure columns, n_eff = 1; for A = I_n, every integral assignment has risk n while uniform fractional routing has risk n/K, a ratio of K for every n.This example shows that increasing the population does not always close the fractional-to-integral gap.Source: §5 · pp. 5–6

6 Routing procedures and certificates

The section pairs a fractional relaxation and finite-agent rounding with a separate quota-preserving swap heuristic and lower-bound checks. It also treats uncertainty in endpoint-error moments and allows concentration when endpoint quality differs.

6.1 Relaxation and finite-agent assignment

  • Conditional-expectation assignment fixes eligible rows one at a time without increasing expected final risk, but it does not preserve hard endpoint quotas.The guarantee applies to feasible fractional assignments with row-wise eligibility and no coupled quota constraints.Source: §6.1 · p. 6

6.2 Quota-preserving exposure swaps

  • For hard quotas, exposure swaps keep endpoint counts fixed and accept the best strictly improving eligible swap; finite-set descent ensures termination, not global optimality.A scalar two-endpoint version contains PARTITION, motivating bounds rather than treating local search as exact.Source: §6.2 · p. 6

6.3 A lower bound with the correct direction

  • A feasible fractional objective alone cannot certify an integral gap; the supporting-hyperplane construction supplies a lower bound for feasible assignments.The bound enforces the eligible-edge inequalities; reported gaps use floating-point numerical bounds checked against small exhaustive problems, not interval-arithmetic certificates.Source: §6.3 · p. 7

6.4 Moment uncertainty and unequal endpoint quality

  • The worst-case moment envelope adds δI to the baseline second moment, but δ needs justification and is not automatically a statistical confidence set.The envelope also applies before averaging randomized assignments.Source: §6.4 · p. 7
  • Diversity is not always preferable: when the cross moment is at least endpoint 1’s second moment, concentration at endpoint 1 is optimal.CER optimizes financial error, not diversity for its own sake.Source: §6.4 · p. 7

7 Computational design

The computational design evaluates routing on controlled synthetic networks and a held-out replay of recorded API errors. The replay reuses responses across institutions and does not represent separately prompted agents or real vendor outages.

7.1 Synthetic portfolio networks

  • The synthetic protocol uses 60 networks of 48 institutions, six assets, and six endpoints, with enumerated single and double removals and controlled exposure and impact heterogeneity.The distributions are not fitted to balance sheets or market depth.Source: §7.1 · p. 7
  • The 11,340 synthetic evaluations are dependent scenarios on 60 independent networks, not 11,340 independent observations.Intervals resample network means and summarize variability under the network generator, not uncertainty about the actual financial system.Source: §7.1 · p. 8

7.2 Recorded API errors and held-out replay

  • The recorded-error replay uses 256 constructed rebalancing tasks and four pinned endpoints, with 128 calibration and 128 test tasks; its held-out comparison pairs model responses across resampled tasks.The loss is averaged over the fixed network/scenario collection, and bootstrap resamples keep fitted policies fixed while conditioning on the calibration split.Source: §7.2 · pp. 8–9
  • The replay applies each fixed assignment to the same held-out error vectors across institutions, so it is a shared-advice replay rather than a measure of separately prompted agents or real vendor outages.Figure 3’s matched-count comparison averages one point per network over removals by size; its right panel tracks means and network bootstrap intervals as common error increases, whose component is invariant to routing.Source: §7.2 · p. 8, Figure 3 · p. 9

8 Results

The quota-preserving swap procedure reduces risk in synthetic outage scenarios, while gains shrink under strongly aligned errors. Fractional routing can overstate diversification, and a held-out replay finds a smaller reduction whose scope is limited by the constructed, single-vendor API evidence.

8.1 Exposure-aware assignment improves the matched-count comparison

  • At β=0.4 and γ=0, mean risk reductions are 6.57% for single removals and 10.53% for double removals, with every endpoint quota preserved.Intervals exclude zero; mean gaps to numerical lower bounds are 2.49% and 2.73%, which measure room to the relaxation rather than exact integral optimality.Source: §8.1 · p. 9
  • At correlation 0.8, benefits fall to 0.43% and 0.79%; homogeneous exposures yield equal matched-quota risks, while feedback variation changes benefit magnitude.The negative controls show that routing cannot remove common error or improve an already identical financial allocation.Source: §8.1 · pp. 9–10

8.2 Fractional policies can overstate diversification

  • The independent-routing gap above the fractional lower bound averages 176.0% at n=4 and 28.0% at n=64, while conditional-expectation assignments reduce it to 134.7% and 5.0%.Every realized conditional-expectation assignment satisfies its finite-agent bound; Figure 4 also shows an orthogonal-exposure case where increasing n does not close the gap.Source: §8.2 · p. 10, Figure 4 · p. 10

8.3 Recorded-error replay: smaller, conditional benefits

  • Held-out replay gives a 3.30% reduction against matched-count routing, with a paired interval of 2.07–4.57%.The replay evaluates held-out API errors; Table 2 distinguishes quota-preserving policies from Common best, which changes counts.Source: §8.3 · p. 10, Table 2 · p. 10
  • Recorded error alignment ranges from 0.848 to 0.999 off diagonal, and the authors state that strong alignment is consistent with smaller gains than under independent errors.The reported alignment is an uncentered cosine, not a Pearson correlation.Source: §8.3 · p. 10
  • Common best reduces loss by 4.53% with different endpoint counts, whereas equal-variance exposure balancing improves overall by only 0.13%, with an interval crossing zero.Ignoring the estimated error structure loses most of the benefit in this replay.Source: §8.3 · p. 11
  • The API replay uses shared recorded errors and does not measure separately prompted agents or real vendor outages; its results do not establish representative model capability or deployed-agent error behavior.The exact deterministic implementation dominates model-only policies, so the replay supports routing calculations on this recorded panel, not a case for LLM arithmetic.Source: §8.3 · p. 11

9 Operational interpretation and limitations

CER is most applicable when a platform knows the financial exposure of decisions, has multiple approved eligible endpoints, and can change routing during disruption. Its evidence remains bounded by synthetic exposures, modeled error assumptions, and limits of second-moment and endpoint testing.

Operational interpretation

  • CER fits platforms that can link decisions to financial exposure and route among approved eligible endpoints during disruption.Its interface can accept exposure estimates, validation errors, eligibility, and capacities, then return assignments, stress metrics, and relaxation gaps.Source: §9 · p. 11

Limitations

  • Synthetic balance sheets and impact coefficients, plus shared errors without private prompts or institution-specific residuals, limit empirical interpretation.The study estimates neither actual AI adoption nor real financial concentration.Source: §9 · p. 11
  • Second moments do not order arbitrary tail probabilities, error moments may drift after outages, and the quota heuristic offers only local guarantees.All measured endpoints use one API vendor, so endpoint omissions do not simulate independent cloud-provider failures.Source: §9 · p. 12

10 Conclusion

The conclusion frames failover as a change in the joint allocation of financial errors, and presents CER as a reproducible way to evaluate contingent routing under declared assumptions. It also makes clear that empirical calibration and independent validation are needed before operational risk-limit use.

10 Conclusion

  • Failover changes the joint allocation of financial errors, so primary endpoint counts and availability alone do not characterize resulting concentration.The conclusion presents the response matrix and exact random-routing premium as tools for making allocation dependence explicit.Source: §10 · p. 12
  • The reported exposure-allocation gains are sharply smaller for common errors, and the conclusion calls for empirical calibration and independent validation before setting operational risk limits.The paper characterizes its result as a reproducible routing stress test under declared assumptions, not a calibrated operational risk estimate.Source: §10 · p. 12
  • The companion repository contains implementation, tests, protocol, prompts, responses, processed moments, results, figures, and manuscript source for offline reproduction.New collection requires an explicit paid-execution flag and separately supplied credential; remote reruns need not return identical text.Source: §10 · p. 12

A.1 Task distribution and model outcomes

The appendix specifies constructed task and network settings, reports feedback-dependent routing reductions and secondary tail checks, and documents independent implementation checks and reproducibility boundaries.

A.1 Task distribution and model outcomes

  • The held-out one-shot calculations report errors in basis points of initial NAV after zero-trade fallback; “valid” means parsed finite output with normal completion, not correctness.Task settings include NAV increments, initial-risky-exposure and target ranges, and fee levels.Source: Table 3 · p. 14, §A.1 · p. 14

A.2 Feedback and granularity

  • 6.57% and 10.53% are the mean single- and double-removal reductions at β=0.4 with zero endpoint correlation.Across β=0, 0.4, and 0.75, the reported reductions vary; greater feedback need not increase relative gain because it changes exposure geometry and baseline risk.Source: §A.2 · p. 14

B Secondary tail checks

  • At γ=0, count-balanced and CER theoretical quadratic risks are 0.41745 and 0.39745, while their Gaussian ES values are 0.45436 and 0.45142.The figure passage reports that CER’s ES improvement is smaller than its quadratic-risk improvement in this secondary check.Source: B Secondary tail checks · p. 14, Figure 6 · p. 15

C Independent checks and reproduction

  • Independent checks enumerate assignments, test the lower bound against integral optima, and verify swap legality and objective changes.Synthetic results are deterministic conditional on the numerical environment, while bootstrap intervals describe only their stated resampling distributions.Source: C Independent checks and reproduction · p. 15

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