Paper Info
Title
Bounds for the sum of dependent risks and worst Value-at-Risk with monotone marginal densities.
Abstract
In quantitative risk management, it is important and challenging to find sharp bounds for the distribution of the sum of dependent risks with given marginal distributions, but an unspecified dependence structure. These bounds are directly related to the problem of obtaining the worst Value-at-Risk of the total risk. Using the idea of complete mixability, we provide a new lower bound for any given marginal distributions and give a necessary and sufficient condition for the sharpness of this new bound. For the sum of dependent risks with an identical distribution, which has either a monotone density or a tail-monotone density, the explicit values of the worst Value-at-Risk and bounds on the distribution of the total risk are obtained. Some examples are given to illustrate the new results. © 2012 Springer-Verlag Berlin Heidelberg.
Year
DOI
Venue
2013
10.1007/s00780-012-0200-5
Finance and Stochastics
Keywords
Field
DocType
complete mixability,monotone density,sum of dependent risks,value-at-risk,value at risk
Mathematical optimization,Upper and lower bounds,Risk management,Monotone polygon,Value at risk,Marginal distribution,Mathematics
Journal
Volume
Issue
ISSN
17
2
1432-1122
Citations 
PageRank 
References 
11
1.22
4
Authors
3
Name
Order
Citations
PageRank
Ruodu Wang14711.75
Liang Peng2121.79
Jingping Yang3112.23