Executive summary
- The pricing unit in war risk is usually the transit, not the annual policy, which changes how frequency must be expressed.
- Event probability for a given voyage depends on route, timing, vessel characteristics, flag, ownership and current conditions in the region.
- Severity is bounded by insured values but shaped by incident type: a total loss, a damage event and a detention have very different distributions.
- Accumulation across simultaneous transits through the same corridor is the dominant capital driver.
- Because data is sparse and conditions non-stationary, uncertainty loading is a first-order component of the price rather than a refinement.
Defining the exposure
The first task is precise exposure definition. A war-risk transit exposure is characterised by the route taken, the time spent in defined high-risk areas, the vessel type and value, the cargo, the flag and beneficial ownership, the operator's security practices, and the specific perils covered by the wording.
Time in area is central. Two vessels transiting the same corridor may face materially different exposure if one passes through in twelve hours and the other calls at a port within the area for three days. Frequency estimates expressed per transit are only comparable when the underlying time-in-area is comparable, which argues for modelling exposure in vessel-hours or vessel-days within defined zones.
Differentiating factors
- Route and zone: specific waters carry materially different risk, and boundaries change with the security situation.
- Vessel profile: type, size, freeboard, speed and value affect both the likelihood of being targeted and the consequence.
- Affiliation: flag, ownership, charterer and recent port calls can affect targeting risk in conflicts where affiliation is a selection criterion.
- Protective measures: convoy participation, routing advice compliance, hardening and embarked security.
- Timing: risk varies with the phase of a conflict and with seasonal or operational patterns.
Frequency and severity
Frequency estimation combines a baseline rate derived from incident data over a defined observation window with adjustments for the current regime and for the specific characteristics above. The baseline is normally expressed as incidents per vessel-transit or per vessel-day within a zone, using a denominator drawn from traffic data.
E[L] = λ(z, t) × d × Σ_k p_k × E[S_k]
- E[L]
- — expected loss for the transit
- λ(z, t)
- — incident intensity per vessel-day in zone z at time t
- d
- — exposure duration in the zone, in vessel-days
- p_k
- — conditional probability that an incident is of type k, given an incident occurs
- E[S_k]
- — expected severity for incident type k, given the insured values at risk
Severity requires conditioning on incident type. A near-miss produces no loss. A strike causing damage produces a partial loss whose distribution depends on the point of impact and the vessel's construction. A constructive total loss caps at insured value plus associated costs. A detention produces loss of hire and, potentially, a claim under different cover. Modelling severity as a single distribution across all incident types obscures these distinct behaviours.
Accumulation and capital
War risk is fundamentally an accumulation problem. Individual transit exposures may be modest; the concern is a scenario in which a corridor is closed, mined or subject to a sustained campaign, affecting a substantial number of insured vessels within a short window. Portfolio management therefore requires continuous visibility of how many insured transits are exposed to each zone at any moment.
- Maintain a live view of in-force transits by zone, with insured values aggregated.
- Define scenarios at portfolio level — corridor closure, multi-vessel campaign, port strike — and evaluate them against the live book, not against an average book.
- Set per-zone aggregate limits, and treat approaching them as a trigger for repricing rather than only for declinature.
- Allocate capital on the marginal contribution of a transit to the portfolio tail, which is far higher when the corridor is already heavily exposed.
From expected loss to quoted rate
The technical premium adds to expected loss the acquisition and administration expenses, the cost of the capital consumed, and a loading for model and parameter uncertainty. In war risk the last of these is unusually large, because incident data is sparse, denominators are uncertain and the regime can change faster than any model recalibration cycle.
Presenting the quote as a range rather than a point, with the drivers of the range identified, is more honest and more useful to the underwriter than a single figure carrying implied precision. Where the market rate sits below the technical range, that fact should be recorded and aggregated so management can see the cumulative position being taken.
Practical example
Suppose an assumed incident intensity of 0.0004 per vessel-day in a defined zone, a transit exposure of 1.5 vessel-days, and a conditional severity structure in which 60 per cent of incidents cause no insured loss, 30 per cent cause partial loss averaging 8 per cent of insured value, and 10 per cent cause total loss. For a vessel insured at 50 million, expected loss per transit is approximately 0.0004 × 1.5 × (0.30 × 4m + 0.10 × 50m) ≈ 3,720.
Adding assumed expenses of 20 per cent, a capital charge reflecting the marginal accumulation contribution, and an uncertainty loading of 40 per cent to reflect sparse data, the technical premium might be several times the expected loss. The magnitude of the uncertainty loading relative to the expected loss is the point of the illustration: in this class, what is not known dominates what is estimated.
Limitations and caveats
- Incident datasets differ in inclusion criteria, geographic coverage and reporting lag, and the choice of source materially changes estimated frequency.
- Traffic denominators are estimated from vessel-tracking data with gaps, particularly where transponders are disabled.
- Historical frequency has limited predictive value across a regime change; model output must be read with current qualitative assessment.
- Sanctions, legal restrictions and policy exclusions can change insurability independently of physical risk.
- Model output supports underwriting judgement; it does not predict specific events.
Conclusion
War-risk pricing is not an exercise in precision. It is an exercise in making an inevitably uncertain judgement structured, consistent, reviewable and comparable across submissions.
The structure — exposure, intensity, severity by type, accumulation, capital, uncertainty — is what allows two underwriters to disagree productively about a parameter rather than unproductively about a number.
References
- International Shipping Facts and Figures — International Maritime Organization
- Review of Maritime Transport — United Nations Conference on Trade and Development
- Insurance Core Principles — International Association of Insurance Supervisors
Author bio
Jonas Mohamed Osman Abdelghafour, known as Yonas Osman is an actuary, FRM and financial risk professional specialising in banking, insurance, model risk, capital modelling and quantitative risk management.