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🔥 '''Damage function''' is a mathematical relationship used in insurance and catastrophe modeling that translates the physical characteristics of a peril — such as wind speed, flood depth, or earthquake intensity — into an expected degree of loss for a given type of property or asset. Sometimes called a vulnerability function or vulnerability curve, it sits at the heart of [[Definition:Catastrophe model | catastrophe models]] and serves as the critical bridge between hazard simulation and financial loss estimation. The function typically expresses damage as a percentage of [[Definition:Total insured value (TIV) | total insured value]], conditional on the intensity of the hazard at the location of the insured risk.

⚙️ In practice, damage functions are developed through a combination of engineering analysis, historical [[Definition:Claims | claims]] data, and expert judgment. A [[Definition:Catastrophe model | catastrophe model]] vendor such as those operating in the property cat space will maintain libraries of damage functions calibrated to specific construction types, occupancy classes, building codes, and geographic regions. When an [[Definition:Insurer | insurer]] or [[Definition:Reinsurer | reinsurer]] runs a portfolio through a cat model, each policy's exposure characteristics are matched to an appropriate damage function, which then converts the simulated hazard intensity at that location into a mean damage ratio and a probability distribution around it. This probabilistic output feeds into the broader [[Definition:Loss distribution | loss distribution]] used for pricing, [[Definition:Reserving | reserving]], and [[Definition:Capital modeling | capital modeling]]. Regulators in [[Definition:Solvency II | Solvency II]] jurisdictions and under frameworks like Japan's solvency regime expect insurers to understand and validate the vulnerability assumptions embedded in the models they rely on.

📊 The accuracy of damage functions directly shapes the quality of catastrophe risk pricing and portfolio management decisions across the global insurance market. After major loss events — Hurricane Andrew in 1992, the Tōhoku earthquake and tsunami in 2011, or European windstorm Lothar in 1999 — model vendors recalibrate their damage functions to reflect observed claims experience, sometimes producing significant shifts in modeled [[Definition:Expected loss | expected losses]]. For insurers and reinsurers, understanding the assumptions inside these functions is not merely a technical exercise; it determines whether [[Definition:Risk-based pricing | risk-based pricing]] is adequate, whether [[Definition:Reinsurance | reinsurance]] purchasing strategies are sound, and whether [[Definition:Regulatory capital | regulatory capital]] reserves appropriately reflect the underlying exposure. Increasingly, climate-related perils like wildfire and inland flood are demanding new or substantially revised damage functions, making this an active area of development in both traditional modeling firms and emerging [[Definition:Insurtech | insurtech]] analytics platforms.

'''Related concepts:'''
{{Div col|colwidth=20em}}
* [[Definition:Catastrophe model]]
* [[Definition:Vulnerability curve]]
* [[Definition:Total insured value (TIV)]]
* [[Definition:Probable maximum loss (PML)]]
* [[Definition:Exposure management]]
* [[Definition:Loss exceedance curve]]
{{Div col end}}

Definition:Damage function - Revision history

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