_Loss due to damage to infrastructure_ (bridges, roads, pipelines, hospitals...). The damage to infrastructure is estimated based on the total damage to the residential buildings in the same area. From the damage information in the past hurricanes in the Caribbean countries (see ECLAC reports), the loss amount from the damage to infrastructure ranges from 15% to 129% of the residential buildings (Grenada 15%, Cayman islands 29%, Jamaica 62%, and Bahamas 129%). Assumptions were made on the ratio of infrastructure loss to residential building loss by hazard and by country.

_Government relief expenditures_ . Government relief expenditures after natural disasters are assumed to be 1% of the total damage to the residential buildings in the same area by referring the information from ECLAC reports.

Government deficit “loss exceedance curves” are built for every Caribbean country and parametric indices are developed for both hurricanes and earthquakes to fit the estimated government deficit loss curve.

It is estimated that short term resources represent up to 20% of the government deficit loss. Therefore, a cost-effective risk financing strategy should be designed to secure funds to be immediately available to cover these losses in the aftermath of a disaster Catastrophe insurance offered by the CCRIF aims at financing hurricanes and earthquake events with a return period between 25 years and 150 years. Each participating country purchased coverage between US$4 million and US$50 million for hurricane risk, and between US$2 million and US$50 million for earthquake risk, with an aggregate coverage not to exceed US$50 million. CCRIF insurance is shown to be cost-effective for this layer of risk, compared to self-retention: the CCRIF premium is shown to be on average 68% lower than the cost of self-retention (World Bank 2007).<sup>4</sup>

# 5. Conclusion

The Arrow-Lind Public Investment Theorem is usually presented as the rationale for countries to apply the policy of risk neutrality in the evaluation of public investment. This paper has discussed how the net present value of a project should be evaluated under uncertainty: it depends on the discount rate, which is independent of the risky project under consideration, and the risk-adjusted expected social net benefit. This benefit is equal to the expected cash flow of the project if and only if the project risk is independent with the macroeconomic risk, leading to the Arrow-Lind theorem.

This assumption of risk neutrality has been challenged when countries are exposed to natural disasters using an alternative model which captures the correlation among individual losses (caused by natural disasters) and the liquidity constraint the government faces. We have shown that countries should evaluate the cost of natural disasters on the basis of a value higher than the expected loss, i.e., the social cost of catastrophic risk bearing is positive, if the catastrophic losses affect a large fraction of the population, the government faces liquidity constraints in the aftermath of a disaster, and the marginal opportunity cost of holding reserves is positive. These conditions are met by most of developing countries exposed to natural disasters, and particularly small state islands. This offers a rationale for the use of ex ante risk financing instruments, including insurance.

> 4 The country still needs to build individual reserves to cover losses caused by events with return periods of  25 years or less.  The optimal risk financing strategy is not discussed here. See Gurenko and Mahul (2003) and Mahul and Gurenko (2006) for a conceptual discussion.

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