Extreme risk analysis of dynamic interdependent infrastructures and sectors of the economy with applications to financial modeling

This dissertation is built on the Inoperability Input-Output Model (IIM), which is an extension to the original Nobel-Prize winning Leontief Input-Output (I-O) model. The IIM transforms the I-O model to an inoperability form so that the ripple effects of an initial perturbation caused by disasters or attacks can be calculated. A dynamic extension to the IIM is introduced in this dissertation. The Dynamic Inoperability Input-Output Model (DIIM) incorporates the concept of industry resilience coefficient to measure the pace of recovery for each industrial sector on the event of an attack. With the DIIM, the recovery paths of the economic sectors are described as functions of time. Inoperability, economic loss, and cumulative economic loss of any sector can be calculated based on the DIIM. In this dissertation, probabilistic perturbations and recovery times that follow certain statistical distributions such as triangular distribution are applied to the IIM and the DIIM. This allows a more accurate input to the model that comes from either expert opinions or empirical databases. Other important aspects of the IIM and the DIIM are also addressed in the dissertation. In particular, modeling various types of recoveries of indirectly affected sectors is discussed in details depending on specific risk scenarios and characteristics of the economic sectors themselves. On occasions when the structure of the economy is changed due to the disasters or the results of risk management options, an analytical framework is given in the dissertation to show how to change the interdependency matrix accordingly for a more accurate representation of the model. The stochastic extension on the DIIM allows the analyst to capture the randomness of the recovery for each economic sector. Finally, a discussion of connecting the macroeconomics to the financial modeling is presented in the dissertation. In particular, a paradigm of applying the industry-type interdependency information to enhance the estimates of portfolio Value-at-Risk (VaR) under the industrial extreme events is introduced in the dissertation. This method will expand the current VaR method to capture the industry-level interdependency besides the correlations among assets in a portfolio given an extreme event.