MSc Risk & Actuarial

Faculty of Commerce, Law and Management · CDU-BUS-RSK-900 · MSc · v1.0.0

The quantities a risk function and an actuarial function sign off: parametric value at risk and expected shortfall, the Basel IRB capital requirement and risk-weighted assets of a corporate exposure, the Bühlmann credibility premium, and the mean, variance and loaded premium of an aggregate loss under the collective risk model.

Lineage

Conquest Designer University, 2026 — authored from the brief, the IFoA/IAA syllabuses and the Basel framework; no prior institution is claimed

Final research project

From a loss distribution to a capital number: value at risk, IRB capital, credibility and the pure premium

Syllabus

Market risk: parametric VaR and expected shortfall, horizon scaling, the normal assumption and its limits
Credit risk: PD, LGD, EAD, maturity, asset correlation and the IRB capital formula
Credibility theory: expected process variance, variance of hypothetical means, the Bühlmann factor
Risk models: compound distributions, the collective risk model, premium principles

Reference

Parametric VaR: V·(z_c·σ·√h − μ·h)
Normal ES: V·(σ·√h·φ(z_c) ÷ (1 − c) − μ·h)
IRB K (corporate): [LGD·N((1−R)^−½·G(PD) + (R/(1−R))^½·G(0.999)) − PD·LGD]·(1 + (M − 2.5)·b) ÷ (1 − 1.5·b) (Basel II ¶272)
Asset correlation: R = 0.12·(1 − e^(−50·PD))/(1 − e^(−50)) + 0.24·[1 − (1 − e^(−50·PD))/(1 − e^(−50))]; b = (0.11852 − 0.05478·ln PD)²
Bühlmann credibility: Z = n ÷ (n + k), k = EPV ÷ VHM; premium = Z·X̄ + (1 − Z)·μ
Collective risk model: E[S] = E[N]·E[X]; Var[S] = E[N]·Var[X] + Var[N]·E[X]²

Units

Parametric value at risk and expected shortfall · IRB capital for a corporate exposure · Bühlmann credibility premium · Collective risk model and loaded premium

Role when narrated: You are a chief risk officer and actuary explaining a capital or premium number to a board risk committee. State the model and its key assumption, show the numbers, and say what would make the answer wrong.

Parametric value at risk and expected shortfall · parametric_var_es

Try with the example

Under a normal model, what loss is exceeded only with probability 1 − c over the horizon, and what is the average loss beyond it?

Reference: J.P. Morgan/Reuters RiskMetrics Technical Document (1996): parametric VaR, square-root-of-time scaling; BCBS (2019) market risk framework: expected shortfall at 97.5%

Returns

z: Standard normal quantile at the confidence level
valueAtRisk: VaR over the horizon
expectedShortfall: ES over the horizon

The example

{
  "portfolioValue": 10000000,
  "dailyVolatility": 0.012,
  "horizonDays": 10,
  "confidence": 0.99,
  "dailyMeanReturn": 0
}

Agents: POST /faculty/msc-risk--actuarial/parametric_var_es with JSON {pan, …inputs} and the x-402-payment header. Manifest.

IRB capital for a corporate exposure · basel_irb_capital

Try with the example

What capital, risk-weighted assets and expected loss does the Basel IRB formula assign to this corporate exposure?

Reference: Basel II (BCBS 2006) ¶272 (corporate risk-weight function), ¶285 (PD floor 0.03%); RWA = K × 12.5 × EAD

Returns

pdUsed: PD after the 0.03% floor
correlation: Asset correlation R
capitalRequirement: K, per unit of EAD
riskWeight: K × 12.5
riskWeightedAssets: K × 12.5 × EAD
expectedLoss: PD × LGD × EAD

The example

{
  "pd": 0.01,
  "lgd": 0.45,
  "ead": 1000000,
  "maturity": 2.5
}

Agents: POST /faculty/msc-risk--actuarial/basel_irb_capital with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Bühlmann credibility premium · buhlmann_credibility

Try with the example

How much weight should this risk’s own experience get against the collective, and what premium results?

Reference: Bühlmann, H. (1967) Experience rating and credibility, ASTIN Bulletin 4(3); IFoA CS2 — the Bühlmann model

Returns

k: EPV ÷ VHM
credibilityFactor: Z = n ÷ (n + k)
credibilityPremium: Z·X̄ + (1 − Z)·μ

The example

{
  "observations": 5,
  "sampleMean": 1200,
  "collectiveMean": 1000,
  "expectedProcessVariance": 40000,
  "varianceOfHypotheticalMeans": 10000
}

Agents: POST /faculty/msc-risk--actuarial/buhlmann_credibility with JSON {pan, …inputs} and the x-402-payment header. Manifest.

Collective risk model and loaded premium · collective_risk_premium

Try with the example

What are the mean and spread of aggregate claims, and what premium does the expected-value principle charge?

Reference: Klugman, Panjer & Willmot, Loss Models (compound distributions); IFoA CS2 — the collective risk model; the expected-value premium principle

Returns

aggregateMean: E[S]
aggregateVariance: Var[S]
aggregateSd: √Var[S]
premium: (1 + θ)·E[S]

The example

{
  "frequencyMean": 2,
  "frequencyVariance": 2,
  "severityMean": 5000,
  "severityVariance": 4000000,
  "loading": 0.2
}

Agents: POST /faculty/msc-risk--actuarial/collective_risk_premium with JSON {pan, …inputs} and the x-402-payment header. Manifest.