Vulnerability and Damage Function Analysis

Vulnerability and damage function analysis estimates the expected loss ratio, the repair or replacement cost expressed as a fraction of an asset's value, as a continuous function of hazard intensity. It is the loss-facing counterpart to fragility analysis: where fragility gives the probability of physical damage states, a vulnerability function gives money, translating intensity directly into expected fractional loss together with its uncertainty. Tiziana Rossetto and Amr Elnashai's 2003 derivation of vulnerability functions for European reinforced-concrete buildings from observed damage is a canonical empirical example, while Charles Kircher, Robert Whitman, and William Holmes's 2006 description of HAZUS earthquake methods shows the standard route of combining fragility curves with damage-state loss factors to build them analytically. The output is the per-typology relationship that, multiplied by exposed value, yields scenario and probabilistic loss. Because it bridges engineering damage and economic consequence, it is the single most influential ingredient in catastrophe and loss models. Getting the mean and the spread of the loss ratio right is what makes a risk model usable for insurance, mitigation, and policy.