Due to the new regulatory guidelines known as Basel II for banking and Solvency 2 forinsurance, the nancial industry is looking for qualitative approaches to and quantitativemodels for operational risk. Whereas a full quantitative approach may never be achieved,in this paper we present some techniques from probability and statistics which no doubtwill prove useful in any quantitative modelling environment. The techniques discussed areadvanced peaks over threshold modelling, the construction of dependent loss processesand the establishment of bounds for risk measures under partial information, and can beapplied to other areas of quantitative risk management.