Ordering Results for Risk Bounds and Cost-efficient Payoffs in Partially Specified Risk Factor Models
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Motivated by the problem of sharp risk bounds in partially specified risk factor models and by the method of cost-efficient payoffs with given payoff structure we introduce and describe some stochastic odering problems for conditionally comonotonic resp. antimonotonic random variables. The aim is to describe the influence of the specified dependence of the components of the random vector X with a benchmark Z on the risk bounds in a risk portfolio resp. on the gain of cost efficiency of the optimal payoffs. We obtain in particular explicit results in dependence on distributional parameters for elliptical models in the case of risk bounds and for the multivariate Samuelson model in the case of cost efficient payoffs.
KeywordsSupermodular function Risk factor models Cost-efficient payoffs Conditionally comonotonic vectors Elliptical distributions
Mathematics Subject Classification (2010)60 E 15 62 P 05 91 B 28 91 B 30
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