Optimal risk reduction and insurance for government infrastructure protection

This study applies the ruin theory to the government’s fiscal problem of infrastructure protection against a risk of destruction associated with reconstruction expenditure. In preparation for the possibility of large-scale expenditure, the government will take out an excess-of-loss (XL) insurance policy as an insured party and, at the same time, invest in physical disaster damage reduction facilities (i.e., “risk reduction”) in advance. The government decides on the layers of risk to be covered by risk reduction, risk retention, and insurance, so as to maximize the expected value of fiscal resources, subject to the constraint that the probability of financial collapse (i.e., “ruin”) is kept below a certain level. Furthermore, the study clarifies the composition of the impacts of risk reduction and insurance on ruin probability and numerically analyzes the optimization problem based on a hypothetical setting constructed using data from Vanuatu. The numerical example demonstrates a case in which the ruin probability rises sharply within specific short intervals of risk reduction and insurance attachment points, surpassing the constraint threshold, suggesting the need for careful selection of countermeasure combinations. It further clarifies that the lower the government’s initial financial reserves, the more extensive the insurance coverage should be.