---
name: actuarial-reserve-uncertainty-quantifier
description: "Quantifies the uncertainty around a loss reserve estimate by running stochastic or bootstrap simulation on a loss triangle, returning a point estimate, coefficient of variation, percentile distribution, and high/low scenario bounds with reserve-range commentary. Use when estimating reserve ranges, building a range of reasonable estimates for an Actuarial Opinion, stress-testing held reserves, or communicating reserve volatility to a CFO or board."
argument-hint: "[loss-triangle] [reserve-basis]"
allowed-tools: ["Read"]
---

# Actuarial Reserve Uncertainty Quantifier

## 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:
1. Fit development factors and compute fitted cumulative values
2. Calculate unscaled Pearson residuals; apply the scale parameter (φ)
3. Resample residuals to generate pseudo-triangles (bootstrap) or apply the Mack variance formula
4. Project each simulated triangle to ultimate, add the **process variance** layer (gamma/over-dispersed Poisson draw)
5. Apply the tail factor and its own uncertainty if development is incomplete
6. 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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## How to use this skill

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**Using in Claude.ai, ChatGPT, Gemini, or other AI tools:**

1. Drag this file into a new chat, or copy and paste its contents
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