Defense Date


Document Type


Degree Name

Doctor of Philosophy


Systems Modeling and Analysis

First Advisor

Dr. Cheng Ly


In the world of finance, appropriately understanding risk is key to success or failure because it is a fundamental driver for institutional behavior. Here we focus on risk as it relates to the operations of financial institutions, namely operational risk. Quantifying operational risk begins with data in the form of a time series of realized losses, which can occur for a number of reasons, can vary over different time intervals, and can pose a challenge that is exacerbated by having to account for both frequency and severity of losses. We introduce a stochastic point process model for the frequency distribution that has two important parameters (average frequency and time scale). The advantages of this model are that the parameters, which we systematically vary to demonstrate accuracy, can be fitted with sufficient data but are also intuitive enough to rely on expert judgment when data is insufficient. Furthermore, we address how to estimate the risk of losses on an arbitrary time scale for a specific frequency model where mathematical techniques can be feasibly applied to analytically calculate the mean, variance, and covariances that are accurate compared to more time-consuming Monte Carlo simulations. Additionally, the auto- and vi cross-correlation functions become mathematically tractable, enabling analytic calculations of cumulative loss statistics over larger time horizons that would otherwise be intractable due to temporal correlations of losses for long time windows. Finally, we demonstrate the strengths and shortcomings of our new approach by using combined data from a consortium of institutions, comparing this data to our model and correlation calculations, and showing that different time horizons can lead to a large range of loss statistics that can significantly affect calculations of capital requirements.


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