Trimming the UCERF3-TD Logic Tree for Rare Portfolio Loss

Porter, Keith Alan

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Trimming the UCERF3-TD Logic Tree for Rare Portfolio Loss Public Deposited

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Citeable URL: https://scholar.colorado.edu/concern/reports/bc386k46p

Abstract

The Uniform California Earthquake Rupture Forecast version 3-Time Dependent is a complex mathematical model of where California’s seismic faults are and how frequently they produce earthquakes. The model is represented by a logic tree with 5,760 leaves, each representing one combination of modeling choices to represent epistemic uncertainties. To use the model in risk analysis, one must often add epistemic uncertainties, such as which of several ground-motionprediction equations to use. Doing so can increase the model size to 172,800 leaves. Each leaf still has explicit uncertainties, often called aleatory uncertainties, such as whether each of 6 million possible earthquakes will occur and the resulting map of spatially correlated shaking. To use the model in practice with all these uncertainties can be computationally demanding. It is desirable to find a subset of epistemic uncertainties that preserve the distribution of important dependent variables. We previously showed how to trim the logic tree to preserve the distribution of expected annualized repair cost to a large portfolio of California buildings. Here we show how to trim the logic tree to preserve the distributions of expected annualized repair cost and of loss with various rare exceedance frequencies: 1 time in 100 years, 250 years, 400 years, 550 years, and 2,500 years. It appears that one can reduce the logic tree to as few as 15 logic tree leaves (from 172,800), varying only ground motion model and ground motion model added epistemic uncertainty, at least for the 400-year and 550-year losses. A hypothetical risk calculation that takes 24 hours for the full model (evaluating all 172,800 leaves) can be reduced to a calculation that takes 8 seconds (for a reduced-order model with 15 leaves). But in all cases examined here, one can trim the logic tree by at least three variables. Because of the exponential relationship between the number of logic tree branches and the size of the model, even trimming three variables can produce a huge savings in computational effort, reducing the number of logic tree leaves to 4% of the size of the full model. Model order reduction can have important financial benefits. With more study, it may be possible to reduce uncertainty around the choice of ground motion model and of added epistemic uncertainty in the ground motion model. Lower uncertainty means thinner tails to the distribution of loss, that is, lower loss associated with rare exceedance rates. If an insurer can reduce its estimate of rare loss, it can buy less reinsurance and save money.

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