Aggregate Rollover Coverage: A First-Best Solution for the Package-Shipping Industry

Jim Sprigg, Pinaki Mitra


When specifying a new coverage option, underwriters must assess its viability with respect to profitability, consumer demand, and regulatory consent. This article specifies a new coverage option for clients of the package-shipping industry, who face transit risks of loss, damage, and delay. Currently, shipping companies and third-party insurers offer pay-as-you-go coverage options under per-claim deductible schemes, which tend to attract “low-volume” clients who suffer fluctuating losses. However, there are no standard coverage options for high-volume clients who find it cheaper to self-insure because their loss experience converges toward its asymptotic properties. In theory, aggregate deductibles offer an efficient alternative to self-insurance. In practice, aggregate deductible schemes are actuarially intractable because underwriters rarely know the precise number of shipments to be insured under a period of performance. This article introduces a “rollover” scheme that allows for aggregate deductibles, derives the conditions for a first-best solution, and describes the economic surplus created by the scheme.

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This work is licensed under a Creative Commons Attribution 4.0 International License.