Purpose
Convert a point reserve estimate or loss triangle into a defensible distribution of reserve outcomes — producing a central estimate, coefficient of variation, percentile bounds, and a range of reasonable estimates that an actuary can carry into reserve reviews, Statements of Actuarial Opinion, and CFO/board conversations about volatility.
When to Use
Invoke this skill when the user asks to:
- Build a reserve range or range of reasonable estimates from a loss triangle
- Calculate the coefficient of variation or volatility around a held reserve
- Run a bootstrap or stochastic simulation on paid or incurred loss development
- Stress-test whether held reserves are adequate at a target confidence level
- Quantify reserve uncertainty for an Actuarial Opinion or quarterly reserve review
- Explain reserve risk and downside scenarios to a CFO, auditor, or board
Inputs Required
Before starting, collect:
- Loss triangle: Cumulative paid or incurred losses by accident/underwriting year and development period (or a stated point reserve estimate if no triangle is available)
- Triangle basis: Paid vs. incurred, accident year vs. underwriting year, and currency
- Line of business: Coverage type and whether it is short-tail or long-tail
- Held reserve / current point estimate: The booked or selected reserve to evaluate against
- Simulation method preference: Mack model, ODP bootstrap, or stochastic chain-ladder (default: ODP bootstrap)
- Target confidence levels: Percentiles required for bounds (default: 50th, 75th, 90th, 95th, 99th)
- Known distortions: Large losses, reinsurance/net-vs-gross basis, tail factor beyond the triangle, or recent reserving changes
If only a point estimate is provided with no triangle, request a CV assumption by line (or apply a documented industry-typical CV) and note that the result is parametric rather than triangle-driven.
Instructions
Step 1: Validate and Diagnose the Triangle
Before simulating, confirm the data supports a credible distribution:
- Check the triangle is square or consistently shaped (equal accident periods and development periods)
- Flag negative incremental development, zero columns, or sparse tail cells that can destabilize bootstrap
- Identify the latest diagonal and whether a tail factor is needed beyond the observed development
- Note whether the basis is gross or net of reinsurance — uncertainty differs materially
- State the deterministic central estimate method (chain-ladder, Bornhuetter-Ferguson) the simulation will sit around
Step 2: Select and Justify the Method
Match method to data conditions:
- ODP Bootstrap (default): Resamples residuals from the chain-ladder fit; best general-purpose choice with a reasonably full triangle. Produces a full predictive distribution including process and parameter variance.
- Mack Model: Closed-form estimate of reserve mean and standard error without simulation; use when a fast analytical CV is needed or when residuals are too sparse to bootstrap reliably. Reports standard error by accident year and in total.
- Stochastic Chain-Ladder / GLM: Use for thin or distorted triangles where parametric structure stabilizes the estimate.
State which method is used, why, and the number of simulations (default 10,000 iterations for bootstrap).
Step 3: Run the Simulation Mechanics
Walk through the computation transparently:
- Fit development factors and compute fitted cumulative values
- Calculate unscaled Pearson residuals; apply the scale parameter (φ)
- Resample residuals to generate pseudo-triangles (bootstrap) or apply the Mack variance formula
- Project each simulated triangle to ultimate, add the process variance layer (gamma/over-dispersed Poisson draw)
- Apply the tail factor and its own uncertainty if development is incomplete
- Aggregate to total unpaid claim distribution across all accident periods
Step 4: Derive the Reserve Statistics
From the simulated distribution, produce:
- Point estimate (mean) and median of the unpaid distribution
- Standard deviation and coefficient of variation (CV = SD / mean) — total and by accident year
- Percentile bounds at the requested confidence levels (default 50/75/90/95/99)
- Range of reasonable estimates: typically the interquartile range or a stated low/high band (e.g., 25th–75th or 10th–90th, labeled explicitly)
- High scenario (e.g., 95th percentile) and low scenario (e.g., 25th percentile) framed as adverse vs. favorable development
Step 5: Assess the Held Reserve
Position the booked reserve within the distribution:
- Report the percentile at which the held reserve sits (its sufficiency probability)
- State whether held reserves fall inside the range of reasonable estimates
- Quantify the margin or deficiency versus the mean and versus the 75th percentile
- Flag if the held reserve sits below the 50th percentile (potential inadequacy) or above the 90th (potential redundancy)
Step 6: Interpret and Translate
Provide actuary-grade and executive-grade reads:
- One paragraph on what the CV implies about volatility relative to typical ranges for that line (short-tail lines run lower CV; long-tail/liability lines run higher)
- Drivers of the spread (immature accident years, tail uncertainty, sparse data, large-loss leverage)
- Stated limitations: model risk, basis of data, tail extrapolation, and that the distribution reflects modeled — not all — uncertainty
Output Format
- Structure: Diagnostic summary → method justification → results table → held-reserve assessment → interpretation
- Length: 800–1,100 words plus tables
- Format: Structured document with a primary results table; percentile bounds and by-accident-year CV in tabular form
- Sections: Data Diagnostic → Method Selected → Reserve Distribution Results (table) → Held Reserve Position → Range of Reasonable Estimates → Interpretation & Limitations
- Tone: Reserving actuary writing for a peer reviewer and a CFO — precise, quantified, explicit about assumptions, never hedging the headline number
Quality Checklist
Before delivering output, verify:
- [ ] The method (bootstrap / Mack / stochastic) is named with a one-line justification tied to the data condition
- [ ] A single point estimate AND a coefficient of variation are both reported as discrete numbers
- [ ] Percentile bounds are labeled with their confidence level (e.g., "90th percentile = X") — not stated as a vague range
- [ ] The held reserve is placed at a specific percentile of the distribution
- [ ] Every key assumption (tail factor, gross/net basis, simulation count, scale parameter) is stated explicitly
- [ ] Limitations section names at least three sources of unmodeled uncertainty
Notes
- The single most common error is reporting only process variance and omitting parameter variance — the ODP bootstrap captures both, and the output should say so.
- Long-tail liability lines routinely show total CVs of 10–25%; a CV under 5% on a long-tail line usually signals an over-smoothed model or a triangle missing real tail uncertainty.
- When no triangle exists and only a point estimate is given, the result is a parametric approximation — label it clearly so it is never mistaken for a triangle-driven distribution.
- For an Actuarial Opinion, the "range of reasonable estimates" is a judgment narrower than the full predictive distribution; present both and keep them distinct.
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