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Methodology and Computing in Applied Probability

, Volume 20, Issue 3, pp 817–838 | Cite as

Ordering Results for Risk Bounds and Cost-efficient Payoffs in Partially Specified Risk Factor Models

  • Jonathan Ansari
  • Ludger Rüschendorf
Article
  • 46 Downloads

Abstract

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.

Keywords

Supermodular 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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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.University of FreiburgFreiburg im BreisgauGermany

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