A duality approach to the worst case value at risk for a sum of dependent random variables with known covariances

2009/12/09 by Brice Franke, Franke, Brice, Michael Stolz +1
Decision Sciences · Economics, Econometrics and Finance · #60E05 #62P05 #90C05 #91G80 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Probability (math.PR) #Risk Management (q-fin.RM) #Risk and Portfolio Optimization #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.0912.1841

openalex publication_date 2009/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose an approach to the aggregation of risks which is based on estimation of simple quantities (such as covariances) associated to a vector of dependent random variables, and which avoids the use of parametric families of copulae. Our main result demonstrates that the method leads to bounds on the worst case Value at Risk for a sum of dependent random variables. Its proof applies duality theory for infinite dimensional linear programs.

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