Appendix 2: Mathematical optimisation methods required for operational risk modelling and other risk mitigation processes

Laureano Escudero

Mathematical optimisation has significant applications in risk measurement and mitigation. In particular, it is used in operational risk modelling for the determination of the severity and frequency distribution functions that best represent the operational risk profile of the institution.

Additionally, mathematical optimisation has other applications in risk management, such as the selection of portfolios of risk exposures (market and credit risk) consistent with risk-averse strategies (Escudero et al, 2014). In fact, the choice of risk exposures can also be applied to operational risk such as in the selection of the optimal insurance programmes for the hedging of operational risk exposures (see Chapter 15).

In this appendix, we present optimisation algorithms for the operational risk distribution function determination. Additionally, we introduce examples of how to implement mathematical optimisation into portfolio selection, in this case the optimisation of credit exposures to obtain a desired risk profile consistent with risk-averse strategies.


The process for determining the optimal distribution

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