Quantification of tail risk to evaluate infrastructure maintenance policies considering time-consistency

Abstract

In civil infrastructure maintenance planning, prevention of severe accidents is essential. Toward that aim, it is necessary to consider the probability of rare events, and risk indices such as value at risk (VaR) and conditional value at risk (CVaR) are frequently employed. However, these indices are not time-consistent. A policy that was initially regarded as optimal may therefore not be optimal when one wants to evaluate the maintenance policy to reduce the probability of tail-risk events, considering policy changes in the future. To eliminate the effect of inconsistency, this study proposes a risk quantification scheme that accounts for the dynamic characteristics of infrastructure maintenance by exploiting the formulation of iterated risk measures as a framework for conventional risk indices such as CVaR. The estimation of the iterated risk measure using a Monte Carlo simulation is costly because it requires a great many samples. To mitigate this problem, the samples are divided into clusters, which enables an efficient identification of samples corresponding to tail-risk events. The performance of the proposed scheme is verified through numerical simulations of road pavement maintenance. The results show that the proposed scheme can evaluate the maintenance policy to reduce the probability of tail-risk events, with consideration for time-consistency.