Paolo Vicig: Imprecise Probabilities in Risk Measurement: a Generalisation of Dutch Risk Measures

 
Abstract: 

 
Imprecise probability theory is a well-grounded uncertainty 
theory, including several independently developed theories as special 
cases (among them, precise probabilities, belief functions, 2-monotone 
capacities, upper and lower previsions, and others). In the realm of 
risk measurement, a risk measure may be interpreted as an upper 
prevision, thus results about imprecise probabilities apply easily to 
this framework, often letting us extend already established concepts. 
In this talk, after recalling basic facts about imprecise probabilities 
and risk measurement, I give an example of such a procedure illustrating 
a generalisation of a family of measures termed Dutch risk measures and 
discussing some of its properties. The generalised version may be viewed 
as a kind of second order risk measure, or a prudential correction of a 
pre-existing measure. It corresponds in insurance premium pricing to 
premium principles which allow a sort of 'double loading' for the 
premium, which is spit with certain rules between an insurer and a 
reinsurer.