Analytic loss distributional approach models for operational risk from the α-stable doubly stochastic compound processes and implications for capital allocation

► We consider Basel II LDA models for Business line/event types. ► A novel class of doubly stochastic alpha-stable family LDA models are derived. ► These models capture heavy tailed loss processes typical of OpRisk. ► These models provide analytic expressions for the compound processes' annual loss density and distributions. ► These models provide analytic expressions for the aggregated compound processes' annual loss models.