Optimize tail risk budget allocation

Allocate a finite mitigation budget across mutually exclusive component mitigation levels to minimize portfolio CVaR while preserving aligned scenario dependence.

Constrained optimization Optimize CTOs Tech CEOs IT managers Team leads Investors

What it's for

Directs limited resilience or security capital toward the combination that reduces joint portfolio tail loss, rather than ranking controls by average loss alone.

What you give it

Inputs split into evidence read from your connected systems, calibration your team owns, and numerical controls that affect precision but never the result's meaning.

Field	Type	Role	Required
budget	number ≥ 0	Your calibration	Yes
max_detail_rows	integer ≥ 1, ≤ 500	Numerical control	Optional
maximum_exact_states	integer ≥ 1, ≤ 2000000	Numerical control	Optional
risk_components	array of objects (3 fields)	Evidence	Yes
scenario_probabilities	array of number ≥ 2 items	Evidence	Yes
tail_probability	number ≥ 0.001, ≤ 0.5	Your calibration	Optional

Each `risk_components` record

Field	Type	Required
id	string (non-empty)	Yes
mitigation_options	array of objects (3 fields)	Yes
scenario_losses	array of number (≥ 2 items)	Yes

Example input

{
  "budget": 60,
  "risk_components": [
    {
      "id": "security",
      "mitigation_options": [
        {
          "cost": 20,
          "id": "basic",
          "loss_reduction_fraction": 0.2
        },
        {
          "cost": 60,
          "id": "strong",
          "loss_reduction_fraction": 0.75
        }
      ],
      "scenario_losses": [
        1000,
        200,
        20
      ]
    },
    {
      "id": "reliability",
      "mitigation_options": [
        {
          "cost": 30,
          "id": "basic",
          "loss_reduction_fraction": 0.35
        }
      ],
      "scenario_losses": [
        400,
        250,
        50
      ]
    }
  ],
  "scenario_probabilities": [
    0.1,
    0.3,
    0.6
  ],

Truncated for display — the full payload is 46 lines.

What you get back

This is the actual output of running the example above — computed by the same function the platform calls, not an illustration.

Example output

{
  "assumptions": [
    "Component loss paths share aligned joint scenarios and mitigation fractions scale the represented component loss without changing other components or scenario probabilities.",
    "Options are feasible, mutually exclusive levels for one component with fully loaded incremental cost; behavioral adaptation and control failure are encoded in residual paths or fractions.",
    "CVaR allocation preserves represented dependence but cannot protect against omitted common causes; the greedy fallback has no global optimality certificate."
  ],
  "component_diagnostics": [
    {
      "baseline_expected_loss": 172,
      "risk_component_id": "security",
      "selected_cost": 60,
      "selected_loss_reduction_fraction": 0.75,
      "selected_option_id": "strong"
    },
    {
      "baseline_expected_loss": 145,
      "risk_component_id": "reliability",
      "selected_cost": 0,
      "selected_loss_reduction_fraction": 0,
      "selected_option_id": null
    }
  ],
  "configuration": {
    "budget": 60,
    "scenario_count": 3,
    "tail_probability": 0.1
  },
  "decision": "tail_risk_budget_allocation_supported",
  "method": "scenario_dependent_cvar_risk_budget_allocation_v1",
  "solver_diagnostics": {
    "estimated_complete_state_count": 6,
    "maximum_exact_states": 200000,
    "optimality_proven": true,
    "solver": "exact_option_state_enumeration"
  },
  "summary": {
    "baseline_cvar_loss": 1400,
    "baseline_expected_loss": 317,
    "cvar_reduction": 750,
    "residual_cvar_loss": 650,
    "residual_expected_loss": 188,
    "selected_option_count": 1,
    "total_cost": 60
  },

Truncated for display — the full payload is 46 lines.

How it works

Constrained optimization — Pick the best feasible option under real limits — budget, headcount, dependencies, capacity — rather than ranking a list and hoping it fits.

1 Freeze aligned component loss paths, feasible mutually exclusive mitigation levels, fully loaded incremental costs, budget, and tail probability over one loss perimeter.
2 Scale component losses by each chosen level, preserve scenario columns, evaluate portfolio CVaR, and enumerate complete option states through the governed boundary.
3 Above the exact boundary disclose marginal-CVaR-per-cost greedy mode, require approved optimization for material allocation, and stress common causes and control failure absent from the scenarios.

Before you trust it

Every tool in the catalog ships with the conditions under which its answer is meaningful — and the conditions under which it should abstain instead of guessing.

Assumptions & guardrails

Objectives use commensurable locally governed value units, constraints reflect real feasibility, and uncertainty covers plausible adverse inputs.
Mitigation fractions are locally validated residual-loss effects, option levels are feasible and mutually exclusive, and cross-component behavioral or technical interactions are encoded in paths.
The recommendation is optimal only for its stated objective, feasible set, evidence, and solver guarantee; it is not a universal management optimum.
CVaR reduction is conditional on represented scenarios; heuristic mode is not globally optimal and an omitted systemic event can overturn the allocation.

Minimum evidence

risk_components: required and organization-defined
scenario_probabilities: at least 2 rows/items
budget: required and organization-defined

How to validate it

Backtest the chosen action against simple feasible baselines on held-out scenarios, sweep costs/constraints/risk tolerance, and require constraint feasibility under adverse inputs.

Calibrating it to your org

Same for everyone

The mathematical kernel, validation rules, method version, and JSON output semantics are organization-independent; no tenant-trained coefficients or company benchmark is embedded in the function.

Specific to you

aligned component loss paths and locally validated residual-loss fraction for every mitigation level
component/loss perimeter, horizon/currency, joint scenarios/probabilities, control interaction/failure, option feasibility, cost, budget, tail level, common causes, and solver promotion

Calibration workflow

1 Define the management decision, target outcome, aggregate unit, privacy boundary, cadence, and prediction/intervention horizon for this organization.
2 Build a tenant-scoped historical cohort using only information available before each prediction or decision; preserve zero periods, censoring, assignment probabilities, and unresolved outcomes when the method requires them.
3 Estimate statistical parameters on training history, but obtain costs, utilities, risk tolerance, practical-effect thresholds, capacity, and policy constraints from accountable decision owners.
4 Validate on later time windows or held-out aggregate units at the deployment grain, against a simple baseline and the function-specific validation strategy.
5 Deploy only if the returned decision clears evidence, overlap, calibration, robustness, and guardrail checks; warning, unsupported, schema-gap, and fallback decisions are abstentions.
6 Monitor realized outcomes, data drift, coverage, and decision regret; recalibrate at a governed cadence or after a detected regime/definition change, never merely because a stakeholder dislikes the result.

Call it from your AI

You don't wire up 388 tools in your MCP client. The GitRevio MCP server exposes 18 tools, three of which let an agent search the catalog, read a tool's schema, and run it — so the assistant finds this one on its own.

gitrevio_capabilities_search
  { "q": "allocate a finite mitigation budget across" }
  → finds "optimize_tail_risk_budget_allocation"

gitrevio_capability_describe
  { "capability_id": "optimize_tail_risk_budget_allocation" }
  → returns the input schema and agent guidance shown on this page

gitrevio_capability_run
  { "capability_id": "optimize_tail_risk_budget_allocation", "arguments": { ... } }
  → returns the result shown above

Works in Claude Desktop, Claude Code, Cursor, Cline, Continue.dev, Goose and Aider. See the MCP server.

Related tools

Aggregate risk register copula

Aggregate risk-register occurrence and lognormal severity marginals through a validated Gaussian copula into expected loss, VaR, CVaR, dependence amplification, and tail shares.

Statistical audit & measurement

Stress test operating plan assumptions

Stress every operating-plan assumption individually and along a common adverse path, exposing remaining outcome headroom and the linear breakpoint at which the plan fails.

Decision analysis

Allocate restless bandit interventions

Allocate scarce recurring interventions across evolving Markov units with Whittle indices, explicit indexability checks, and paired policy simulation.

Sequential Bayesian & bandits

Attribute commercial dependency tail loss

Calculate expected loss, VaR and CVaR for commercial value concentrated in shared technical components, then allocate every modeled tail-loss dollar exactly once across components with normalized negative-log survival hazard rather than overlapping leave-one-out sensitivities.

Forecasting & survival

Audit commercial resilience claim integrity

Audit resilience ROI claims against a unique commercial-source to technical-component graph: recompute each action's avoided loss under joint failure scenarios, cap support at graph-derived value, detect duplicate effects, probability drift and weak evidence, and prevent overlapping component benefits from being sold twice.

Network & dependency analysis

Audit decision rank robustness smaa

Measure rank acceptability, regret, pairwise dominance, and central winning weights under uncertain criterion scores and bounded stakeholder weights.