Mathematical Models for Operational Risk Management

Abstract

The thesis presents the state-of-the-art mathematical statistical models for Operational Risk measurement and management as well as the organisational and managerial processes supporting the creation of risk OR measures. We emphasise the most interesting probabilistic ideas employed in the field and apply the models on real data; these are used in the actuarial modelling paradigm following a Loss Distribution Approach. Extreme Value Theory, convolution transforms and copulæ theory will all be part of OR analysis to arrive to a regulatory risk measure. The thesis accompanies the theoretical modelling part with the management processes that are needed to implement these models in financial institutions, along with the primary risk mitigation techniques used against OR events. Finally, in light of the recent consultations carried out by the Bank for International Settlements regarding the partial substitution of actuarial models, we will also reflect on the differences, commonalities, and limitations of present and future OR modelling. The thesis is organised as follows. Chapter I introduces the major risk types institutions face. Chapter II describes the non-actuarial risk measurement techniques used by banks without internally developed actuarial models. The central mathematics of the thesis is presented and applied in Chapter III. Chapter IV compares the present modelling techniques with recently proposed modifications. Chapter VI treats the managerial aspects of OR and Chapter VI studies risk mitigation tools usually adopted. We conclude in Chapter VII with reflections and final comments.