Risk, tails & resilience
What the bad case costs, how correlated your failures are, and which policies survive being wrong.
42 of 388 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.
Allocate restless bandit interventions
Allocate scarce recurring interventions across evolving Markov units with Whittle indices, explicit indexability checks, and paired policy simulation.
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.
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.
Audit decision rank robustness smaa
Measure rank acceptability, regret, pairwise dominance, and central winning weights under uncertain criterion scores and bounded stakeholder weights.
Audit extreme metric tail dependence
Detect extreme metric co-exceedances beyond independence with empirical tail coefficients, permutation inference, practical magnitude gates, and FDR control.
Audit metric regime stability
Detect practical structural breaks across aggregate metric histories with recursive max-CUSUM search, moving-block null resampling, and familywise false-alarm control, then identify the defensible baseline regime.
Audit portfolio dependency value double counting
Reconcile project and dependency business-case claims to governed unique benefit sources under coherent scenarios, quantifying naive, unique, duplicated, and unassigned value before portfolio prioritization.
Audit scenario tree decision integrity
Audit whether an adaptive management or capital policy is executable rather than clairvoyant: reconcile terminal probability mass, tree depth and unique node ancestry; require identical actions and information releases for indistinguishable histories; reject actions whose declared evidence is revealed only later; and retain unverified scenario exposure.
Audit service continuity recovery evidence integrity
Audit whether each critical service has a current, independently reviewed recovery plan whose complete capability/dependency path, backup, restore, failover, communications, RTO and RPO were proven in a recent production-representative exercise.
Audit technology loss scenario integrity
Audit a technology loss-scenario ledger as a complete, zero-inclusive, point-in-time financial perimeter: reconcile every expected aggregate exposure and source, freeze scenario/currency/price basis, enforce evidence and privacy, and detect economic-loss lineage reused outside an explicit shared-loss group.
Audit technology risk appetite integrity
Audit whether board technology-risk appetite is executable rather than rhetorical: verify approval and point-in-time lineage, reconcile the root to finance limits, cover every aggregate risk unit exactly once, validate an acyclic owner/action limit tree, cap unsupported diversification credit and surface every breach with an executable escalation.
Calculate financial value of modularity
Value modular architecture as a portfolio of exercisable future-change options, comparing architecture-specific cost, lead time, throughput capacity, discounting, value decay, downside CVaR, and the break-even modular investment.
Calculate technology economic capital
Calculate expected loss, loss VaR/CVaR, unexpected-loss economic capital, capital charge and technology RAROC under coherent finance-owned scenarios; count shared platform/provider loss once and reconcile it to aggregate units with exact or seeded-permutation Shapley allocation.
Calculate technology risk capacity and headroom
Translate technology loss into board-level risk capacity by jointly stressing liquidity, earnings, covenant and capital absorption; report expected loss, exact probability-mass VaR/CVaR, unexpected-loss capital, appetite headroom, binding constraints and the maximum supported loss multiplier before the approved breach probability fails.
Calculate value of management flexibility
Price only executable management flexibility on one coherent scenario set: compare a frozen static plan, a nonanticipative adaptive policy and a perfect-information upper bound; separate expected flexibility from remaining information value, tail underperformance and tail regret; quantify liquidity-risk reduction; and refuse value when policy integrity, evidence or dominance fails.
Detect operational critical slowing down
Detect early-warning patterns associated with an aggregate system losing resilience before a possible regime transition: locally detrend rolling windows, track rising lag-one autocorrelation, variance, and spectral reddening, compare endpoint shifts with a frozen reference regime, and control multiplicity under a circular moving-block bootstrap.
Estimate decision reversal probability
Estimate how often planned evidence would reverse the current decision under a correlated Bayesian preposterior model, while separating fragility, regret, and net information value.
Estimate engineering extreme value risk
Estimate rare incident, delay, loss, or pipeline-duration return levels with peaks-over-threshold generalized-Pareto fitting, bootstrap uncertainty, and threshold-stability diagnostics.
Estimate engineering portfolio VAR
Estimate correlated cost, schedule, success, value-decay and portfolio downside VaR/CVaR with initiative tail attribution.
Estimate portfolio diversification benefit
Measure coherent portfolio diversification by comparing joint-scenario CVaR with standalone CVaRs and reconciling Euler tail-risk contributions, stress loss, and concentration gates.
Estimate real option abandonment boundary
Learn a continuous-state project abandonment policy with cross-fitted least-squares Monte Carlo, explicit salvage economics, option uplift precision, support warnings, and boundary-shape diagnostics.
Estimate systemic portfolio contagion
Estimate nonlinear financial distress propagation across a directed portfolio network under coherent joint shocks, separating direct from contagion loss and reporting CVaR, convergence, spectral instability, tail attribution, and finite-round loss influence.
Forecast customer facing service interruption loss
Forecast customer-facing outage frequency, duration, SLA credits, interrupted revenue, churn exposure and total financial VaR/CVaR using local zero-inclusive service history, compound log-normal severity and coherent shared-dependency events.
Forecast organizational change load capacity
Forecast whether the organization's planned portfolio of migrations, launches, reorganizations, policy changes, and platform transitions exceeds aggregate operating capacity: select a saturating distributed-lag change-load model on pretest history, beat an autoregressive baseline on later periods, then simulate peak strain and limit-breach probability.
Infer stability selected temporal metric graph
Infer a compact aggregate temporal dependency graph with a chronologically held-out ridge VAR, moving-block coefficient bootstrap, practical-effect stability selection, and false-discovery control.
Optimize commercial resilience portfolio
Select a budgeted, capacity-feasible technical resilience portfolio directly on a deduplicated commercial exposure graph, combining simultaneous failures and multiple mitigations multiplicatively, enforcing CVaR and critical-loss gates, returning a cost-loss-tail Pareto frontier, and disclosing exact or deterministic beam search.
Optimize deadline recovery plan
Choose a budget-feasible deadline recovery plan over a dependency DAG using correlated triangular task durations, uncertain acceleration effects, common random numbers, probability-gain-per-cost search, and backward pruning.
Optimize distributionally robust action
Choose the action with the best worst-case expected value when scenario probabilities may vary inside a KL-divergence ambiguity set.
Optimize risk adjusted technology portfolio
Choose a dependency- and exclusion-feasible technology investment portfolio on an expected-value, cost, shared-loss CVaR and economic-capital frontier, maximizing net value after a finance-owned capital charge while enforcing budget, capital, tail-loss and RAROC hurdles with exact or disclosed beam search.
Optimize robust intervention portfolio
Choose a dependency-safe action portfolio that balances expected and worst-case outcomes.
Optimize service continuity investment portfolio
Choose one production-exercised continuity posture per service-risk unit by maximizing retained business value minus direct/common interruption loss, full cost and CVaR under RTO, RPO, residual-risk, control, dependency, budget and resource constraints.
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.
Optimize technology risk limit allocation
Allocate scarce aggregate technology risk limits across discrete locally executable operating envelopes, preserving option relations and common loss once; maximize expected net value after a capital charge subject to nominal, expected-loss, CVaR, economic-capital and RAROC appetite, then reconcile selected unit capital with exact or seeded Shapley allocation.
Optimize time consistent capital policy
Optimize a finite multistage capital policy that can actually be followed: attach action bundles to observable scenario-tree nodes, enforce local budgets/capacity plus pathwise dependencies and exclusions, roll scenario cash and terminal enterprise value, constrain liquidity chance and recursively nested conditional CVaR, and disclose exact global enumeration or deterministic beam fallback.
Recommend safe contextual bandit action
Recommend contextual aggregate interventions with Bayesian reward learning only inside a posterior logistic harm constraint, explicitly falling back to a governed baseline when no arm is safe enough.
Reconcile hierarchical delivery forecasts mint
Reconcile independently produced portfolio, product, team, repository, or workstream forecasts into one additive hierarchy using shrinkage MinT: learn the cross-level residual covariance on training forecasts, prove coherence, gate accuracy on later untouched periods, and return coherent current forecasts with uncertainty intervals.
Simulate dependency cascade risk
Stress-test correlated baseline failures and directed dependency cascades with portfolio loss VaR/CVaR and risk contributions.
Solve belief state management policy
Solve a finite-horizon partially observable management problem over calibrated latent operating states and quantify the value of adaptive observation.
Solve distributionally robust markov policy
Solve a discounted Markov policy against simultaneous L1 transition-confidence sets derived from empirical state-action counts.
Solve entropic risk sensitive markov policy
Solve a finite-horizon Markov policy under exponential downside utility and compare it with the risk-neutral policy using paired Monte Carlo lower-tail CVaR.
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.