Multivariate stochastic copula-based deterioration models in infrastructure economic risk management

This research explores the current practices in infrastructure Life-Cycle Cost Analysis as well as the Cost Function Modeling in Infrastructure Project Finance. It suggests that more comprehensive and realistic methods are needed to model and simulate the correlated degrading conditions during the infrastructure project life-cycle. This research proposes a new framework in Infrastructure Economic Risk Management, which models infrastructure life term degradation stochastically through the use of empirical models. Two stochastic models are developed: a Hybrid Multivariate Non-Homogeneous Markov Chain model (HMNMC) and a Copula-Based Multivariate Ordered Probit model (CBMOP). The first model, the HMNMC model, is a hybrid model since it combines the state based degradation model with the duration based degradation model using a nonlinear optimization approach to overcome the disadvantages of limited observed data. Furthermore, this model represents the actual infrastructure degradation over a long period of time in a more realistic way than the frequently used homogeneous Markov Chain models. Peculiarly, the HMNMC model uses empirical copulas to capture the correlations among infrastructure subsystems. The second model, CBMOP, improves the established statistical model — Ordered Probit Model to account for the time dependency of the infrastructure degradation. The uniqueness of the second model is the introduction of a new empirical approach to build a Multivariate Ordered Probit Model using Copula. More specifically, it models and correlates the random errors in the linear regression equations by fitting them into an Empirical Copula. This process results in a time dependent and correlated Multivariate Ordered Probit Model. This research then validates a general framework for applications of the developed models to the infrastructure LCCA and BOT Project Finance. Finally, an application of the models to a case example on the National Bridge Inventory (NBI) database is performed and the results are compared. It is envisaged that these research findings would be of great value in future bridge management practice.