Risk allocation in a public-private catastrophe insurance system: An actuarial analysis of deductibles, stop-loss, and premiums

A public-private (PP) partnership could be a viable arrangement for providing insurance coverage for catastrophe events, such as floods and earthquakes. The objective of this paper is to obtain insights into efficient and practical allocations of risk in a PP insurance system. In particular, this study examines how the deductible and stop-loss levels (retentions) for, respectively, the insured and the insurer, relate to the corresponding maximum required coverage and premium amounts under the 99.9% tail value at risk (TVaR) damage constraint. A practical example of flood insurance in the Netherlands is studied in which the (re)insurance could be provided either by a risk-averse (private) or a risk-neutral (public) agency, which could result in large differences in premiums.