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Quote Engine Active Set: Peak Concurrently-Live Quotes

Add Two Binary Strings

Almgren-Chriss Static Optimal Execution Trajectory

Shrinkage Blend of Two Alpha Sources with Z-Score Normalization

American Put Pricing via Longstaff-Schwartz Least-Squares Monte Carlo

Antithetic Variates Variance Reduction

Array Product Except Self

Arrival Price vs TWAP Decision under Alpha Decay

Dual-Benchmark IS — Arrival Price vs Interval VWAP

Arithmetic-average Asian Call MC Pricing with Antithetic Variates

Geometric-average Asian Call: Closed-form Black-Scholes Pricing

As-of Merge — Attach Most-Recent Mid-Price to Each Trade

As-of Merge — Trades against Quotes

Per-Asset Beta to a Benchmark Portfolio

Bachelier (Normal) Implied Vol from a Quoted Call

Credit-Based Backpressure — Replay Producer/Consumer Events into a State Trace

Daily Backtest with Overnight Borrow Cost

Multi-Feed Bar-Sync Period: LCM Modulo p

Up-and-out Barrier Call MC Pricing with Daily Monitoring

Basel III Output Floor — Capital Requirement Across Phase-In Schedule

Basel IRB Risk-Weighted Asset for a Corporate Exposure

Basel VaR Backtest Traffic-Light Zones

Basel VaR Backtest — Traffic-Light Zone and Capital Multiplier Add-On

Bermudan Put on a CRR Tree with Selective Early-Exercise

Binary-State Strategy — Best PnL With Post-Exit Cooldown

Best Single Trade in a Day

Best Trades With K Transactions and Fee

Bilateral CVA and DVA Under Independence: Two Discounted Time-Profile Sums

Leftmost Index via Binary Search (bisect_left)

Backward Induction on a Generic Binary Tree

Invert Binary Tree (Mirror)

Maximum Depth of a Binary Tree (Recursive)

Symmetric Binary Tree Check

CRR Binomial Tree for an American Put

Analytical Binomial Credit-Loss VaR for a Uniform-PD Homogeneous Portfolio

American Put Pricing on a CRR Binomial Tree

CRR Binomial Tree for a European Call

Black-Scholes Call Implied Vol via Bisection

Per-Position Flag Bitmask Queries

Blocked Time-Respecting CV: Contiguous Folds with Train-Before-Test

Convexity of a Fixed-Coupon Bond

Modified Duration of a Fixed-Coupon Bond

Modified Duration on a Discrete Zero Curve

Bond Portfolio Key-Rate Duration Hedge via Least Squares

Continuous-Compounded Yield-to-Maturity for a Fixed-Coupon Bond

Periodic Yield To Maturity of a Fixed-Rate Coupon Bond via Bisection

Bounded K Transactions: 2D DP for Maximum Profit

Multi-Strike Portfolio with Per-Strike Share Cap (Bounded Knapsack)

Best Realized PnL Bound Under K Disjoint Round-Trips with Per-Roundtrip Impact Cost

Box-Muller: Uniform Pairs to Standard-Normal Pairs

Brinson-Hood-Beebower Three-Effect Attribution

Brownian Bridge Running Minimum Survival Probability

Black-Scholes Delta for Batched Calls and Puts

Black-Scholes European Call and Put Pricing in Batch

Black-Scholes Gamma and Vega in Batch

Black-Scholes Implied Vol from a Quoted Call or Put via Newton-Raphson

Black-Scholes Rho for Batched Calls and Puts

Black-Scholes Theta for Batched Calls and Puts

Trade-Size Tier Histogram via Right-Inclusive Edges

Bucket-Sort P&L Histogram

Discrete Bucket-Vega Hedge Allocator

Budgeted Whole-Share Portfolio

Build Largest P&L Signal-Strength String

Detect Butterfly-Arbitrage Violations on a Call-Price Strike Grid

Calmar Ratio — Annualized Return over Maximum Drawdown

Canonical Ticker-Symbol Form — Cross-Venue Dedup

Pre-Aggregation Bucket Labels: Canonical-Form Group IDs for Multi-Venue Symbols

Capital Conservation Buffer: MDA Factor Quartile Schedule

Card Shuffle Bias Detection

Cash-or-Nothing Digital Call: Closed-form Black-Scholes Pricing

Periodic IRR of an Equally-Spaced Cashflow Stream Under the Standard-Project Assumption via Bisection

Per-Tenor Flat-Hazard Survival Curve from a CDS Spread Term Structure

Implied Default Probability from a CDS Spread

CDS-Implied Cumulative Default Probability via the Credit-Triangle Approximation

Par CDS Spread Implied by a Cumulative Default Probability via the Inverse Credit Triangle

CDS Upfront Fee from Par Spread, Standard Coupon, and Risky PV01

Choueifaty Diversification Ratio of a Gaussian Portfolio

Christoffersen Conditional Coverage LR_cc Joint Statistic for VaR Backtesting

Christoffersen LR_ind Independence Statistic for VaR Backtesting

Christoffersen Independence Test for VaR Breach Clustering

CIR Short-Rate MLE Calibration on a Historical Series

Sample from a Clayton Copula

Locally-capped Cliquet Call MC Pricing with Antithetic Variates

Closer-Stronger Bid Distance (Bidirectional): Min of Prev / Next Strictly-Higher Bid

Closest Trade Pair to Target Notional

Cluster Correlated Tickers

Compact a Ring-Buffer of Ticks into Evenly-Bucketed Time Slices

Component VaR Decomposition (Euler Allocation)

Component VaR Decomposition for a Gaussian Portfolio

IC-IR-Weighted Composite of Three Sub-Factors

Compound-Poisson Aggregate-Loss Variance for an Operational-Risk LDA Period

Conditional Drawdown at Risk

Conditional Scenario-Tree Probability-Weighted PnL Aggregation

Consolidated Best-Bid Stream Across K Venue Quote Feeds

European Call MC with Geometric-Asian Control Variate

Empirical Copula Tail-Dependence Coefficients

Cornish-Fisher VaR

Cornish-Fisher VaR Adjusted for Skewness and Excess Kurtosis

Covariance to Correlation Matrix

Aggregate Multi-Desk VaR from Standalone VaRs and a Loss-Correlation Matrix

Correlated Factor-Shock Monte-Carlo for Stress P&L

Factor Cluster Count: Connected Components on a Thresholded Correlation Graph

Count K-Tick Windows With Every Quote Inside the Tolerance Band

Win-Count Leaves on a Forward Scenario Tree

Count of Strictly-Positive Net-Inflow K-Period Windows

Count Regime Paths Satisfying Constraint

Counterparty Activity Shift: Largest Trade-Count Differential Across Two Sessions

Counterparty Gross-Notional Aggregator: Magnitude-Sorted Roll-Up

Credit Expected Loss under Multiplicative PD and LGD Stress Shocks

Credit Portfolio Expected Loss and Naive Unexpected Loss

Credit Portfolio Concentration: HHI and Effective Number of Counterparties from Per-Obligor EAD

Credit Portfolio MC Loss Distribution (Single-Factor Gaussian Copula)

Cross-Tape Buy-Above-Sell Routing-Quality Alert Count

Cross-Feed Cumulative-Count Lead Exchanges

Worst Cross-Feed Closest-Match Paired Lag

Cross-Feed Tick Match Count Within Tolerance Window

Cross-Feed Unmatched Tick Counts Per Side Within Tolerance

Cross-Gamma 2D Shock-Grid PnL via Bilinear-Quadratic Taylor

Cross-Gamma PnL Attribution: Two-Asset Greek Decomposition

Cross-Sectional Demean of an Alpha Factor

Rank-to-Percentile Transform on a Cross-Section of Alpha Factors

Cumulative PnL Drawdown Alert: Sorted Indices Underwater Beyond Threshold

Cumulative PnL Zero-Crossings: Count Sign Flips of the Backtest Equity Curve

Cumulative Default Probability from Marginal Hazard Rates: Term-Structure Composition

Cumulative Volume Snapshot

Cumulative VWAP at Each Tick

Currency Arbitrage Cycle Detection (Bellman-Ford on Log Rates)

DAG Multi-Worker Topological Schedule

DAG Schedule on K Machines with Critical-Path Priority

Days Until a Better PnL

Counterparty Rotation Indicator: Day-Over-Day Symmetric-Difference Series

Decile-Spread Forward Return Averaged Across Dates

Recursive Binary Decision-Tree Evaluator

Deduplicate a Replayed Tick Stream by (ts, exchange-seq), Latest-Ingest Wins

Deepest No-Drawdown Leaf on a Forward Scenario Tree

Pairwise Default Correlation from One-Factor Gaussian-Copula Bivariate-CDF Inputs

Bump-and-Revalue Finite-Difference Delta

Discrete Delta-Hedge Path Simulation with Transaction Costs

Per-Side Dense-Rank Annotation for the Day's Blotter

Diebold-Mariano Test for Two VaR Forecasts via Pinball-Loss Differential

Digital Cash-or-Nothing Call Monte Carlo with Antithetic Variates

Open-Order Dashboard Tile: Distinct Symbols Currently In Play

Divide-and-Conquer Sum Tree (Parallel Reduction Simulation)

Dollar Gamma Across a Strike Ladder

Double-No-Touch Pricing via Antithetic-Variate Monte Carlo

Downsample a Tick Stream into OHLCV Bars (Right-Closed)

Earliest End-Day Reaching A Cumulative Inventory Target From Each Starting Day

Sequenced Limit Orders — Earliest K-th Fire Day With Per-Order Threshold And Cooldown Gap

Earliest K-Period Window Whose Cumulative Return Meets A Sum Target And Whose Worst Single Period Stays Above A Floor

Earliest K-Day Window Whose Population Variance Strictly Exceeds A Spike Threshold

Edit Distance for Ticker-Symbol Mapping

Weighted Edit Distance with Per-Character Cost Matrices

PV-Weighted Effective Maturity M for IRB Credit RWA Input

Effective Number of Independent Obligors from Uniform Pairwise Default Correlation

Empirical CDF Tail Probability at a Fixed PnL Threshold

Empirical Copula via Per-Column Uniform Rank Transform

Empirical Inverse-CDF Marginal Mapping (Copula Pipeline, Step Two)

Empirical Mean Excess Function for POT Threshold Selection

Empirical Upper-Tail-Dependence Coefficient from Bivariate Samples

Enumerate Hedge Decompositions

Equal-Risk-Contribution Portfolio Weights

Toy Equal-Risk-Contribution Solver (Fixed-Point Iteration)

Expected Shortfall Calibration Backtest via Exceedance-Day Ratio

Estimate Barrier Hit Probability

Euler Risk Allocation for Portfolio Volatility

European Call Monte Carlo with Antithetic Variates

European Call Price via Monte Carlo

Fit a Gumbel (GEV, ξ=0) to Block Maxima by Method of Moments

Hill Estimator for the Tail Index

Peaks-Over-Threshold GPD Fit by Method of Moments

Exponentially-Weighted Sharpe Ratio

RiskMetrics EWMA Volatility Forecast

EWMA Volatility Update

EWMA-Weighted Historical VaR

Excess Returns Over a Benchmark

Composite Broker Execution-Quality Score with Direction-Aware Z-Score Blend

Optimal Execution Trajectory Under Hard Per-Bucket Volume Caps

Expected Portfolio RWA After H Rating-Migration Steps

Rolling Historical Expected Shortfall (CVaR)

Expected Value at Root of Scenario Tree

Factor Dependency Topo Order: Deterministic Min-Heap Kahn for Nightly Rebuild

Per-Factor Risk Attribution Under a Linear Factor Model

Factor-Shock Scenario P&L on a Linear Factor Model

Fan-Out / Fan-In Coordination — Event Replay

Fill Attribution by Parent Order ID

Per-Venue Fill Rate with Wilson Confidence Intervals

Filtered Historical Simulation VaR

Find the Pivot Index of a P&L Stream

Find Third Largest Distinct

First Day Cumulative PnL Crosses Threshold

First Duplicate Order ID

Fills-Audit Frequency Probe: First Order-ID Whose Lifecycle Hits Exactly k FIX Events

OU First-Passage Time by Monte Carlo

First Unique Character

FIX-Style Trailing Checksum Verify: Trinary Label Per Pipe-Delimited Message

FIX-Style Tag Extract: First Value for a Numeric Tag in a Pipe-Delimited Message

Fixed-strike Lookback Call MC Pricing with Discrete Monitoring

FizzBuzz

Pricing a Floating-Rate Note from a Zero Curve

Fork-Join Segment Stats (Welford Pairwise Merge)

Forward-Fill Missing Minutes Within a Trading Session

Cross-Hedge Residual Variance and Explanatory Power

Black-Scholes PnL Attribution: Delta, Gamma, Vega, Theta

GARCH(1,1) Multi-Step Variance Forecast

Gaussian-Copula Correlated Samples via Cholesky Factorisation

Sample from a Gaussian Copula

GCD of Share Lots — Round-Lot Reconciliation

Universal Tick Unit: GCD of Per-Venue Tick Sizes

Greenwald-Khanna Streaming Quantile Summary

GPD Tail-VaR Extrapolation under the POT Framework

Count Connected Components in an Undirected Graph

Detect a Cycle in an Undirected Graph

Greedy Coin Change on a Canonical Denomination Set

Minimum Fee-Tier Selection to Cover a Target Volume Range

Walking the Book: Greedy Minimum-Cost Fill

Minimum Platforms for a Railway Schedule

Minimum Cost Path Through a Grid

Maximum P&L Path Through a Grid

Groupby-Mean by Key with a Min-Count Gate

G-SIB Systemic-Importance Score with Substitutability Cap

Bivariate Gumbel-Copula CDF Closed-Form Evaluation

HDR Histogram Recorded-Value Bucket Index and Quantile Estimate

Single-Sigma Black-Scholes Calibration to a Strike Grid

Heston Calibration Residual in Implied-Vol Space

Highest K-Day Range

Hill Estimator for the Tail Index of a Heavy-Tailed Loss Distribution

Historical Expected Shortfall at Multiple Confidence Levels

Historical Expected Shortfall

Historical Scenario Replay: Worst-K Rolling-Window PnLs

Historical Stress Loss Replay

Historical VaR at Multiple Confidence Levels

Historical VaR for a Long-Only Portfolio

Rolling Historical VaR Track

IC-Weighted Alpha Signal Combination

Iceberg Order Book — Replenishment & Fills

Idiosyncratic Volatility Factor — Rolling Residual Std After Market Beta

Post-Trade Impact Attribution Across Venues with a Cross-Venue Interaction

Implementation Shortfall — Three-Component Attribution

Black-Scholes Implied Volatility on a Strictly Increasing Price Curve via Bisection

Implied Volatility with Newton + Bisection Fallback

Newton-Raphson Implied Volatility from a Quoted Call

Vega-Weighted Average Implied Volatility Across a Strike Grid

Implied Volatility via Bisection

Implied Volatility via Newton's Method

Importance Sampling for Deep OTM Monte Carlo

Incremental Largest Cluster Size: Streaming Union-Find on a Factor-Pair Edge Tape

Component VaR per Asset (Euler Decomposition)

Incremental VaR of a Candidate Trade

Annualized Information Ratio

Information Ratio of an Active-Return Series

Insert and Merge Order-Book Price-Level Intervals

Inverse Percentile Rank of Daily PnL Against Reference Distribution

Black-Scholes Call Implied Vol via Brent's Method (scipy.optimize.brentq)

Black-Scholes Call Implied Vol via Hybrid Newton-Raphson with Bisection Fallback

Batch IV Pre-Flight — No-Arbitrage Bracket Classifier

Black-Scholes Put Implied Vol via Bisection

Black-Scholes Call Implied Vol via the Secant Method

Jarrow-Rudd Binomial Tree for European Options

Merton Jump-Diffusion European Call via Monte Carlo

Jump Game — Can You Reach the Last Index

Jump Game II — Minimum Jumps to Reach Last Index

K-Day Momentum Hits

K-Day Rolling Mean Filter

Kendall's Tau-a Rank Correlation on a Bivariate Sample

Budget-Constrained Ticker Selection (0/1 Knapsack)

Minimum Eating Speed (Binary Search on the Answer)

Kupiec POF Likelihood-Ratio Statistic for VaR Backtesting

Kupiec Proportion-of-Failures (POF) Test Statistic

Lag/Lead Shift by Key — Within-Group Time-Series Offset

Largest Factor Cluster Size: Maximum Connected Component on a Thresholded Correlation Graph

Largest Divisible Pair (Sort + Scan)

Largest Rectangle in Order Book Depth

Largest Volume Rectangle in a Histogram

Basel III Liquidity Coverage Ratio with HQLA Caps

Leaky-Bucket Rate Limiter as Admission Control

Leisen-Reimer Binomial Tree for European Options

Basel III Leverage Ratio

Basel III Leverage Ratio: Credit Conversion Factors over Off-Balance Items

LGD Beta-Distribution Calibration via Method of Moments

LGD via Collateral-Then-Unsecured Recovery Waterfall

LGD Aggregation with Collateral Recovery Cascade

Lifetime Expected Loss with Survival Weighting and Per-Period LGD/EAD

Limit-Order Fill Simulation against High-Low Bars

Linear Market-Impact Cost of a Child-Order Schedule

Liquidity Coverage Ratio: HQLA, Inflow Cap, and Net-Outflow Floor

Longest Consecutive Sequence (Hash Set)

Longest Contiguous Window of Volumes Within an Impact Budget

Longest Palindromic Substring

Longest Stable Trading Streak

Longest Stair-Stepping Subsequence Of Cumulative-PnL Reports Under A Minimum-Gain Gate

Longest Sub-Window Beating a PnL Target via Monotonic-Stack on Prefix Sums

Longest Substring Without Repeating Characters

Longest Trailing Window Whose Absolute-Return Sum Stays Within a Volatility Budget

Look-Ahead Bias Detector via Lagged-Correlation Comparison

Fixed-Strike Lookback Call Pricing via Monte Carlo

Lopez I Magnitude Loss Function for VaR Backtesting

Robust Cross-Sectional Z-Score via Median and MAD

Mahalanobis Distance via Cholesky Forward-Solve

MapReduce Group-By Count (Two-Phase Aggregation)

Marginal Default Probability from a Cumulative-PD Term Structure: Inverse Bootstrap

Marginal VaR by Asset (Closed-Form Gradient)

Marginal VaR Sensitivity for a Gaussian Portfolio

Match Bid and Ask Snapshots

Maximum Cumulative Carry Under a Bounded Sign-Flip Budget

Maximum Realised Cumulative Return When Allowed To Skip At Most K Periods

Winning-Streak Counting — Maximum Disjoint Positive-Sum Runs of Minimum Length

Maximum-Diversification Portfolio (Choueifaty-Coignard)

Max Drawdown Decomposition

Maximum Drawdown Duration on the Equity Curve

Maximum Grid PnL Path With At-Most-K Cell Skips (Right/Down)

Semi-Analytic Call Price on the Max of n iid Lognormals

Max Non-Overlapping Trade Windows

Single-Session Child-Order Scheduling with FIX Reconfigure Gap

Maximum Profit Over Bounded-Drawdown Window

Disjoint Risk-Bucket Hedge Selection under a Bucket-Budget Bitmask

Max-Reward Sequence Alignment Across Trade-Action Streams

Maximum Total Reward From Timestamped Trade Candidates Under A Compliance Hold-Period Gap

Three-State Action Path — Max Cumulative Reward With Flat Per-Flip Switching Penalty

Max Sum of a Min-Step-Monotone Reward Subsequence (Stair-Step PnL Ceiling)

Max Sum of Fixed-Size Window

Maximum Child-Order Throughput With Per-Order Durations And A FIX-Session Gap

Maximum Concurrent Trades

Mean-Excess Curve Across a Threshold Grid

Mean-Reversion Factor — Residualized Last-K Return

Long-Only Mean-Variance Efficient Frontier

Merge Per-Day Bar Shards into a Sorted Timeseries

Merge K Quote Streams with Lineage

Merge K Sorted Trade Streams

Merge K Per-Venue Trade Tapes Into One Chronological Stream

Top-N Recent Items From Per-Source News Feeds

Merge Overlapping Quote-Validity Windows

Merge Two Sorted Lists — Iterative Two-Pointer

Merge Two Trade Tapes

Min Cancels for Quote Stability

Throttle-Window Compliance Replay: Minimum Order Cancels

Min Cash Buffer to Survive

Min Contracts to Cover Greek Buckets via Bitmask BFS

Minimum Cost for Train Travel Passes

Regime-Stability Segmentation — Fewest Bounded-Spread Runs Over A Return Stream

Earliest Second Where the Algo Hits Its Volume Target Without Tripping the Slippage Cap

Minimum Constant Maker Fill-Rate to Meet a Parent-Order Deadline Under Per-Minute Supply Caps

Position-Band Governance: Minimum Flatten-Resets to Stay Inside [-L, +L]

Minimum Flips for Monotone Up-Day Pattern

Best Single Round-Trip Realized PnL Under a Minimum-Holding-Period Compliance Rule

Min Hops to Core Factor Set: Multi-Source BFS on a Factor-Similarity Graph

Minimum Knight Moves — BFS on an Infinite Board

Calibrating the Minimum Leverage Cap for a Target Risk Budget

Largest Uniform Collateral Haircut Covering a Liability via Bisection

Minimum Max-Drawdown Across Root-to-Leaf Paths

Tear-Sheet Bucketing — Fewest Strictly-Positive-Sum Cover Chunks With Per-Block Length Cap

Hedge-Inventory Replenishment: Minimum Top-Ups to Stay Non-Negative

Min Replenishments to Avoid Stockout

Minimum Concurrent Streaming Jobs for Execution Windows

Smallest Router Count under a BFD Load-Cap Assigner via Bisection

Minimum Routers with FIX-Session Setup Delay

Smallest Slippage Cutoff Meeting a Target Absolute Weighted Cost via Bisection

Minimum Spread Tolerance for Target Fill Rate

Min-Stack with O(1) get_min

Smallest Stress Severity Factor Where a Counterparty First Breaches Its Cap

Minimum Tickers for Liquidity Coverage

Two-Asset Minimum-Variance Portfolio (Closed Form)

Long-Only Minimum-Variance Portfolio Weights

Smallest Slice Length Whose Every Window Meets a Volume Target

Minimum Window Substring

Mincer-Zarnowitz OLS Regression for VaR-Forecast Unbiasedness

Misra-Gries (k-1)-Counter Heavy-Hitters Over a Trade-Tape Stream

Modigliani M-Squared — Vol-Rescaled Risk-Adjusted Return

Monte-Carlo VaR for a Multi-Asset Portfolio

Order-Event Footprint: Most-Frequent Consecutive Event-Pair

Tape-Anomaly Detector: Most-Repeated Trade Fingerprint

Multi-Horizon Gaussian VaR Scaling

Multi-Leg Implementation Shortfall — Basket Covariance Attribution

Multi-Level Monte Carlo for a European Call

Multi-Period DP for Optimal Execution Under Impact and Risk

Multi-Period Impact P&L with Exponential Decay Between Periods

Multi-Factor Scenario PnL Vector via Linear Taylor

Rank Features by Histogram-Estimated Mutual Information with the Target

End-of-Day Net Positions from a Raw Trade Tape

Net Stable Funding Ratio: ASF over RSF Aggregation

Group-Neutralize a Factor by Sector Tag

Time-to-New-All-Time-High: First Future Index Strictly Above the Running Peak

Next Depth-Jump within a Forward Window: Bounded-Distance Ratio-Threshold Scan over a Best-Bid-Depth Tape

Next Greater Quote Timestamp

Next Smaller Element Index

Min Rebalance Windows To Remove

Min Intervals To Remove For Non-Overlap

Notional by Venue, Ranked

Basel III Net Stable Funding Ratio (NSFR)

Omega Ratio of a Return Series at a Threshold

Lag-1 Sample Autocorrelation of a Time Series

Online Cumulative Bollinger Bands: Welford-Recurrence Band-Pair Stream

Online EWMA Covariance Pair — Cross-Asset Hedge-Ratio Building Block

Online EWMA Residual Stream — Surprise-vs-Prior Exponential-Weight Mean

Online EWMA Variance — Recency-Weighted Volatility Tracker

Running Mean and Mean Absolute Deviation

Online Median of Slippage

Online PCA via Oja's Rule (Streaming PC1)

Online Running Excess Kurtosis via Welford-Style Fourth-Moment Recurrence

Online Running Sample Skewness via Welford-Style Third-Moment Recurrence

Online Streaming Mean, Variance, Skewness, and Excess Kurtosis (Welford-Pebay)

Online Z-Score Anomaly Flag

Online Z-Score Outlier Flagger: Welford-Cumulative Anomaly Detection on a Tick Stream

Optimal Cooldown Period Trades

Optimal Strike Allocation in Option Spread

Order Queue Priority

Router Reliability Check: Count Orphan Cancellations

Classical Gram-Schmidt Orthogonalization of Priority-Ordered Alpha Signals

Pairwise Rating-Transition Probability at Horizon: Single Entry of Markov Chain M^H

Pancake Sort: Flip Sequence

Parallel Pairwise Mean Merge with Kahan Compensation

Parametric Gaussian Expected Shortfall from Caller-Supplied Moments

Rolling Parametric VaR (Normal)

Pareto Tail VaR via Hill-Estimator Extrapolation

Partition Orders to Minimize Basis Mismatch

Pascal's Triangle Row in O(k) Space

Closed-Form 2x2 PCA Eigendecomposition

PCA Explained-Variance Ratio for Top-k Components

Optimal Ledoit-Wolf Shrinkage (Frobenius)

Multi-Period Default Probability from a Rating-Transition Matrix

Post-Earnings Announcement Drift Signal (D+1 to D+60 Excess Return)

Peak Inventory Day After Batched Range-Update Trades

Percent-Change from a Configurable Base

Quantile Estimate from Pre-Bucketed Histogram Counts

Linear-Interpolation Percentile of Trade PnL

Survival Probability at Multiple Horizons under a Piecewise-Flat Hazard Term Structure

Pinball (Quantile) Loss for VaR Forecast Backtesting

Cache-Aware Pipeline Replay — Minimum Re-run Set with Input-Hash Chaining

Research Pipeline DAG — Cascade-Invalidate Downstream of a Failed Task

Research Pipeline DAG — Compute the Next-Runnable Set

Standardized VaR-Forecast Residual Stream — De-Mean Then Divide By Vol

Long-to-Wide Pivot — Reshape a (Date, Ticker, Value) Panel into a Matrix

Greek-Based PnL Attribution

Greek-Attribution P&L Explain with Residual Diagnostic

Aggregate Book Delta per Underlying

Portfolio Expected Loss by Bucket: PD x LGD x EAD Waterfall

Aggregate P&L Up a Portfolio Hierarchy Tree

Multi-Asset Portfolio Parametric VaR (w^T Σ w)

Whole-Share Portfolio Allocator under a Single-Name Cap

Per-Asset and Portfolio Cap Clamping for Target Weights

Position Fingerprint Grouping

Position P&L With Transaction Fees

Reactive POV Schedule with Min/Max Catch-Up Bounds

Power-of-Two Bit Check

Pre-Trade Multi-Leg Impact Budget Check (Square-Root Model)

Prev-Stronger Bid Distance: Time Since the Last Strictly-Higher Bid Print

Price-Time Priority Queue — Order Book Replay

Primality Test by Trial Division

Priority-Driven Task Scheduling with Deps on a Worker Pool

Pro-Rata Allocation — Single-Level Fill Distribution

Probability of Reaching a Target Leaf Set on a Binary Scenario Tree

Prune Binomial Tree to Min Nodes

Purged k-Fold CV with Embargo

Purged k-Fold Cross-Validation for Time-Series ML

Present Value of a Post-Default Recovery Cash-Flow Stream

Quadratic-Taylor Scenario PnL Vector via Delta and Gamma

Quartile Pack with IQR from Per-Period Returns

Queue Position Fill Probability — Closed-Form Under Poisson Arrivals

Quintile (k-tile) Bucketing of a Cross-Sectional Factor

Best-of-N Rainbow Call MC Pricing with Cholesky and Antithetic Variates

Random Walk Hitting Probability

Range-Accrual Note Pricer via Daily-Monitoring MC with Antithetic Variates

2D Range Sum via Prefix Table

Rank-Average Multi-Factor Signal Combination

Cross-Sectional Rank Bucketing into Deciles with Ordinal Tie-Breaks

Rank Records by Multi-Key Tie-Break Rule

Spearman Rank Correlation with Average-Rank Tie Breaking

Spearman Rho and Kendall Tau-b: Dual Rank-Correlation Diagnostic for the Copula Pipeline

RankGauss Transform on a Cross-Section of Alpha Factors

Rank-Disagreement Count: Pairwise Inversions Between Expected and Realized Strategy Rankings

Rank Strategies by Sharpe with Vol Tiebreak

Multi-Step Rating Distribution Propagation: Markov Transition Forward H Steps

Realign K Trade Tapes to a Global Clock with Per-Tape Offsets

Realized-Volatility Jump Test (Barndorff-Nielsen and Shephard)

Turnover-Aware Rebalance on Bucketed-Signal Change

Forward Recovery Distance: Days Until Cumulative Gain Clears Delta

Recursive Walk Down a Hierarchical Rebate-Tier Tree

Per-Node Conditional Expected Leaf Payoff on a Scenario Tree

Regime-Conditional Historical Expected Shortfall

Regime-Conditional Historical VaR

Regime Transition Path Count: Modular DAG Walk Enumeration with Distinguishable Catalysts

Removing K Digits — Smallest Result