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Skillsadvanced-short-term-actuarial-mathematics

advanced-short-term-actuarial-mathematics

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Updated 10-16 04:56

About this skill

Advanced Short-Term Actuarial Mathematics

When to Use

  • Select and justify severity families (parametric tails, mixtures) and frequency models (Poisson, negative binomial, mixtures)
  • Build aggregate loss models: compound distributions, normal approximation limits, FFT/simulation concepts
  • Apply credibility (Bühlmann, Bühlmann-Straub, limited fluctuation) and experience rating math
  • Structure ratemaking: pure premium, loss ratio, trend, on-level, indicated change logic
  • Explain short-term reserving at the mathematical level (chain ladder factors, expected loss ratio)
  • Estimate parameters (MLE), run goodness-of-fit and diagnostics, interpret residuals and tail fit
  • Compute risk measures (VaR, TVaR) and relate them to capital concepts at a technical level
  • Connect modeling choices to pricing and reserving workflows; hand execution to actuarial-analyst

When NOT to Use

  • Life insurance, annuities, long-term care, or life contingencies (mortality, reserves by policy) → life-health-insurance or longevity-focused skills
  • Triangle workbooks, exhibit production, statutory tie-outs, or model run packs only → actuarial-analyst
  • Appointed actuary opinions, regulatory sign-off, or enterprise capital policy → actuary, appointed-chief-actuary
  • Enterprise assumption governance, assumption papers, and change control → assumption-setting
  • P&C coverage wording, claims handling, underwriting authority, or DOI filing narrative → property-casualty-insurance
  • Exam cram or past-exam solutions as the sole deliverable (support professional application; exam study is secondary)
  • General data science, ML pipelines, or quant research without actuarial loss-model framing → data-scientist, quantitative-researcher
  • Chart design and dashboard craft only → data-visualization
  • Credential pathway and exam strategy only → associate-actuary

Related skills

Need Skill
Workpapers, triangles, exhibits, model I/O, analyst QA actuarial-analyst
Sign-off, capital overview, governance memos actuary
Appointed actuary / chief actuary regulatory framing appointed-chief-actuary
ASA/FSO exam pathways and professional standards associate-actuary
Assumption governance and enterprise change control assumption-setting
P&C lines, underwriting, claims, and policy mechanics property-casualty-insurance
Statistical/ML modeling beyond standard actuarial methods quantitative-researcher
General ML and predictive pipelines data-scientist
Charts, dashboards, and visual design data-visualization

Core Workflows

1. Problem framing (ASTAM-aligned)

Before fitting distributions:

  1. Horizon — Short-term (annual or shorter); accident vs calendar year; prospective period for pricing
  2. Random variables — Severity (X), frequency (N), aggregate (S=\sum X_i); clarify i.i.d. assumptions
  3. Data grain — Claim-level vs policy-period; censoring/truncation (deductibles, limits)
  4. Deliverable — Model spec, parameter estimates, diagnostics, business interpretation—not filing sign-off
  5. Peer execution — Route spreadsheet builds and filing exhibits to actuarial-analyst

See references/astam_scope_and_principles.md.

2. Severity and frequency modeling

  1. Explore severity empirical tail; candidate families (exponential, gamma, lognormal, Pareto, generalized Pareto for tail)
  2. Explore frequency dispersion; test Poisson vs negative binomial vs mixtures
  3. Document moments, tail indices, and parameter stability across segments
  4. State dependence assumptions (usually independence for standard compound model; flag if copula needed → escalate)
  5. Summarize model selection criteria (AIC/BIC, Anderson–Darling, QQ plots)—not a single automatic pick

See references/severity_and_frequency_models.md.

3. Aggregate and compound losses

  1. Define compound model (S = X_1 + \cdots + X_N)
  2. Apply normal approximation when conditions hold; state when it fails (heavy tail, low frequency)
  3. Outline FFT and simulation approaches for discrete/continuous severity (conceptual steps)
  4. Relate percentiles of (S) to risk measures and reinsurance layers (technical only)

See references/aggregate_loss_models.md.

4. Credibility and experience rating

  1. Choose limited fluctuation, Bühlmann, or Bühlmann-Straub per homogeneity and data structure
  2. Compute credibility weights (Z); define complement (manual, industry, prior)
  3. Blend observed experience with complement for pure premium or loss ratio
  4. Document heterogeneity across classes/years and structural parameters

See references/credibility_and_experience_rating.md.

5. Ratemaking and short-term reserving (math level)

  1. Pure premium indication: frequency × severity with documented adjustments
  2. Loss ratio and on-level premium; trend to prospective period
  3. Indicated change vs constraints; distinguish technical indication from implemented rate
  4. Reserving: chain-ladder factor algebra, expected loss ratio method—link full triangle work to actuarial-analyst

See references/ratemaking_and_trend.md.

6. Estimation, diagnostics, and risk measures

  1. Fit via MLE (or method of moments where standard); report standard errors when available
  2. Run goodness-of-fit and tail diagnostics; document limitations
  3. Compute VaR and TVaR at stated confidence levels; interpret for capital layers (non-regulatory)
  4. Package assumptions, alternatives, and sensitivity for actuary review

See references/estimation_diagnostics_and_risk_measures.md.

Deliverable standards

Deliverable Minimum content
Model specification Random variables, independence, censoring/truncation, segment definition
Parameter table Estimates, method, uncertainty, stability notes
Diagnostics QQ/PP, GOF tests, tail plot, A/E if applicable
Business bridge Pure premium, credibility blend, indicated change or reserve factor (math only)
Limitations Data volume, tail extrapolation, regime change, outlier treatment

Label output as technical modeling support, not actuarial opinion, legal advice, or filed regulatory submission.

Assignment type matrix

Trigger phrase Primary workflow Lead reference
severity model / tail behavior Severity families and selection severity_and_frequency_models.md
frequency model / negative binomial Frequency and dispersion severity_and_frequency_models.md
aggregate loss / compound distribution Compound (S) aggregate_loss_models.md
Bühlmann credibility Credibility weights credibility_and_experience_rating.md
experience rating / pure premium Rating blend credibility_and_experience_rating.md
ratemaking / trend / on-level Indication math ratemaking_and_trend.md
chain ladder / ELR (math) Reserving formulas ratemaking_and_trend.md
MLE / goodness-of-fit Estimation and GOF estimation_diagnostics_and_risk_measures.md
VaR / TVaR Risk measures estimation_diagnostics_and_risk_measures.md

When to load references

  • Scope, ASTAM alignment, principles → references/astam_scope_and_principles.md
  • Severity and frequency → references/severity_and_frequency_models.md
  • Aggregate and compound losses → references/aggregate_loss_models.md
  • Credibility and experience rating → references/credibility_and_experience_rating.md
  • Ratemaking, trend, reserving math → references/ratemaking_and_trend.md
  • Estimation, GOF, VaR/TVaR → references/estimation_diagnostics_and_risk_measures.md