Portfolio Risk Capstone

This capstone asks for one decision: what reserve, reinsurance structure, and capital evidence should Harbour Mutual take to its risk committee? The answer must connect every number to a loss definition and information date.

Case file

Harbour Mutual is a fictional UK motor insurer. Inputs are synthetic and intentionally incomplete so that judgement is visible.

A. Existing claims at 31 December 2023

Cumulative paid loss (£m):

Earned premium (£m) is 324, 365, 380, and 580 respectively. Pricing's expected loss ratio is 86%.

B. Prospective 2024 portfolio

Baseline expected prospective gross loss is

This is future 2024 risk. It must not be added to the reserve for pre-2024 accidents unless the requested financial view explicitly combines them.

C. Treaty candidates

1. no reinsurance;
2. 40% quota share;
3. £20,000 xs £20,000 per loss;
4. one student-designed occurrence or aggregate layer with complete wording assumptions.

Market premium is deliberately absent. State the break-even ceded loss first, then identify what quotation or pricing assumptions are needed for a recommendation.

Task 1 — Reserve past events

Reproduce and explain:

Then:

1. validate the data contract;
2. show factor/prior selections and one sensitivity each;
3. backtest at least one historical diagonal;
4. select a central estimate or range;
5. distinguish process, parameter, model, and data uncertainty.

The selected answer need not equal any single method, but the reconciliation must be numerical.

Task 2 — Model prospective claims

Specify:

Minimum analysis:

• justify Poisson or negative-binomial frequency using exposure and dispersion;
• compare at least two same-mean severity families in the tail;
• state deductible, limit, inflation, and event treatment;
• use a chronological or scenario holdout concept;
• report expected loss and at least one 99% tail measure.

Short explanation standard

Weak: “Lognormal fits insurance claims.”

Strong: “Gamma and lognormal models share the £5,000 mean, but the lognormal's 99% quantile is materially higher; because the decision prices a £20,000 attachment, survival calibration around £20,000–£40,000 receives more weight than histogram fit below £5,000.”

Task 3 — Apply treaties exactly

Write every candidate as a function before simulation:

For the designed treaty, state:

• per-risk, per-occurrence, or annual-aggregate subject loss;
• attachment, limit, and annual aggregate limit;
• reinstatements and premium treatment;
• gross/net, currency, indexation, and exclusions;
• recovery timing and counterparty assumption.

Compare gross and net mean, SD, VaR, TVaR, attachment, and exhaustion. Do not rank treaties until reinsurance economics are added.

Task 4 — Challenge diversification

Run at least three scenarios:

1. baseline independent frequency/severity;
2. same marginals with a shared catastrophe state;
3. claims inflation plus a fixed nominal layer.

Explain which movement comes from:

• changed marginal frequency/severity;
• changed dependence;
• changed contract response;
• Monte Carlo noise.

Use common random numbers for treaty comparison and show simulation stability at increasing sample sizes.

Task 5 — Put the annual model on a path

Choose initial capital and a net premium process. Estimate finite-time ruin over one and five years, then compare with any available classical benchmark.

The conclusion must state why the output is not automatically:

• IFRS 17 fulfilment cash flow or risk adjustment;
• Solvency UK SCR;
• a complete internal model;
• a liquidity assessment.

Required submission

Concise writing is assessed through evidence density, not omission. Every exhibit must state units, information date, gross/net basis, and source.

Assessment rubric

Evidence desk: current material

Use current sources to challenge the model, not to import unexamined parameters:

Undergraduate and postgraduate routes

• Undergraduate: deterministic reserving, two severity models, simulation with analytical moment checks, and clearly bounded recommendation.
• Postgraduate: stochastic reserve uncertainty, censored/truncated likelihood, tail threshold sensitivity, common-shock dependence, and parameter/model uncertainty propagated into net capital.

Both routes must be transparent and reproducible. Complexity earns credit only when it changes the decision or the confidence placed in it.

Final oral defence: five questions

1. Which single assumption has the largest decision impact, and how do you know?
2. What new data would most reduce uncertainty?
3. Which result is directly observed, estimated, simulated, or externally sourced?
4. Under what scenario does your treaty recommendation reverse?
5. What claim are you deliberately not making?

Core sources

• CAS downloadable reserving datasets
• ABI — 2025 motor claim payouts and comparability note
• Swiss Re Institute — natural catastrophes in 2025
• Bank of England — Solvency UK insurance-sector reporting