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

actuarial-analyst

actuary

appointed-chief-actuary

associate-actuary

assumption-setting

property-casualty-insurance

quantitative-researcher

data-scientist

data-visualization

Core Workflows

1. Problem framing (ASTAM-aligned)

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

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

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)

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

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

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

references/estimation_diagnostics_and_risk_measures.md

Deliverable standards

Assignment type matrix

severity_and_frequency_models.md

severity_and_frequency_models.md

aggregate_loss_models.md

credibility_and_experience_rating.md

credibility_and_experience_rating.md

ratemaking_and_trend.md

ratemaking_and_trend.md

estimation_diagnostics_and_risk_measures.md

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