Expected Annual Loss (EAL) is the average loss that a structure, portfolio, or region is expected to incur per year from seismic events, computed by integrating the loss curve over all possible hazard levels. It is a fundamental metric for risk-informed decision-making and insurance pricing.
Expected Annual Loss (EAL), also called Average Annual Loss (AAL), is the average loss β expressed in monetary terms or as a percentage of replacement value β that an asset, portfolio, or region is expected to incur per year due to seismic events. It is computed by integrating the loss curve over all hazard levels: EAL = β« Loss(IM) Β· |dΞ½(IM)/dIM| dIM, where Loss(IM) is the expected loss at hazard intensity IM and Ξ½(IM) is the annual rate of exceedance of IM. Equivalently, EAL can be computed as the sum over all scenarios of the probability of each scenario times the expected loss in that scenario. EAL captures both the frequency and the severity of potential losses, providing a single metric that can be compared across different assets, portfolios, or mitigation strategies.
EAL is a central metric in catastrophe risk modeling and insurance. In the insurance industry, EAL is used to price premiums, to determine capital requirements (e.g., under Solvency II or RBC frameworks), and to evaluate the profitability of different portfolios. EAL is also used in probabilistic risk assessment frameworks such as those developed by FEMA (HAZUS), GEM (OpenQuake), and commercial catastrophe modeling firms (RMS, AIR, CoreLogic). These frameworks compute EAL for portfolios of buildings, infrastructure, and populations, producing risk maps that show how expected losses vary across a region. EAL is often reported alongside other risk metrics β such as Probable Maximum Loss (PML), which describes the loss at a given return period (e.g., 475-year or 2,475-year), and Tail Value at Risk (TVaR), which describes the average loss in the worst-case scenarios beyond a given percentile. Together, these metrics provide a comprehensive picture of risk.
EAL is used for several decision-making purposes. In mitigation planning, EAL is used to evaluate the cost-effectiveness of retrofit, relocation, or other risk reduction measures β comparing the reduction in EAL to the cost of the intervention. In insurance and reinsurance, EAL informs pricing, capital allocation, and portfolio management. In government policy, EAL informs decisions about building codes, land-use planning, and public investment in resilience. In infrastructure management, EAL prioritizes investments across different assets and networks. In international development, EAL informs the allocation of resources for disaster risk reduction. Key challenges in EAL estimation include: (1) the sensitivity of EAL to the tail of the loss distribution β EAL is dominated by frequent, moderate events, but the most catastrophic scenarios, though rare, contribute to risk in ways that EAL alone does not capture; (2) the uncertainty in hazard, exposure, and vulnerability models, which propagates to EAL; (3) the treatment of indirect losses (business interruption, supply chain disruption), which are often excluded from EAL estimates; (4) the treatment of time-dependent effects (recovery, reconstruction, migration), which are rarely modeled explicitly; and (5) the interpretation of EAL β it is an average, not a prediction of what will happen in any given year. In Iran, EAL studies have been conducted for major cities, particularly Tehran, and for critical infrastructure. The Tehran Earthquake Scenario β a joint Iranian-Japanese study β estimated EAL for buildings, casualties, and infrastructure damage in Tehran under a major earthquake scenario, informing emergency planning and retrofit priorities. Modern Iranian practice increasingly uses HAZUS, OpenQuake, and locally developed risk models, with growing attention to the integration of EAL with resilience metrics and to the treatment of uncertainty.