National governments are key actors in managing the impacts of extreme weather events, yet many highly exposed developing countries -- faced with exhausted tax bases, high levels of indebtedness, and limited donor assistance -- have been unable to raise sufficient and timely capital to replace or repair damaged infrastructure and restore livelihoods after major disasters. Such financial vulnerability hampers development and exacerbates poverty. Based on the record of the past 30 years, this paper finds many developing countries, in particular small island states, to be highly financially vulnerable, and experiencing a resource gap (net disaster losses exceed all available financing sources) for events that occur with a probability of 2 percent or higher. This has three main implications. First, efforts to reduce risk need to be ramped-up to lessen the serious human and financial burdens. Second, contrary to the well-known Arrow-Lind theorem, there is a case for country risk aversion implying that disaster risks faced by some governments cannot be absorbed without major difficulty. Risk aversion entails the ex ante financing of losses and relief expenditure through calamity funds, regional insurance pools, or contingent credit arrangements. Third, financially vulnerable (and generally poor) countries are unlikely to be able to implement pre-disaster risk financing instruments themselves, and thus require technical and financial assistance from the donor community. The cost estimates of financial vulnerability -- based on today's climate -- inform the design of "climate insurance funds" to absorb high levels of sovereign risk and are found to be in the lower billions of dollars annually, which represents a baseline for the incremental costs arising from future climate change.