A reconciliation of the top-down and bottom-up approaches to risk capital allocations

Two overarching approaches to allocate the aggregate risk capital stand out nowadays. These are the top-down approach that entails that the allocation exercise is imposed by the corporate centre, and the bottom-up approach that implies that the allocation of the aggregate risk to business units is informed by these units. Briefly, the top-down allocations start with the aggregate risk capital that is then replenished among business units according to the views of the centre, thus limiting the inputs from the business units. The bottom-up approach does start with the business units, but it is, as a rule, too granular, and so may lead to missing the wood for the trees.
In this research project, we will connect the bottom-up approach to allocate the aggregate risk capital to a general class of Dirichlet distributions defined on the n-dimensional simplex. The new class, which is called herein ``mixed-scaled Dirichlet distributions’’ contains the classical Dirichlet distribution as a special case, exhibit a multitude of desirable closure properties, and emerge naturally within the multivariate risk analysis context.

Intern: 
Batur Celik;Nawaf Mohammed
Faculty Supervisor: 
Ricardas Zitikis;Edward Furman;Ida Ferrara
Province: 
Ontario
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