Convexity of Chance Constraints with Dependent Random Variables: The Use of Copulae

René Henrion () and Cyrille Strugarek ()
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René Henrion: Weierstrass Institute for Applied Analysis and Stochastics
Cyrille Strugarek: Credit Portfolio Management, Calyon Credit Agricole CIB

Chapter Chapter 17 in Stochastic Optimization Methods in Finance and Energy, 2011, pp 427-439 from Springer

Abstract: Abstract We consider the convexity of chance constraints with random right-hand side. While this issue is well understood (thanks to Prékopa’s Theorem) if the mapping operating on the decision vector is componentwise concave, things become more delicate when relaxing the concavity property. In an earlier paper, the significantly weaker r-concavity concept could be exploited, in order to derive eventual convexity (starting from a certain probability level) for feasible sets defined by chance constraints. This result heavily relied on the assumption of the random vector having independent components. A generalization to arbitrary multivariate distributions is all but straightforward. The aim of this chapter is to derive the same convexity result for distributions modeled via copulae. In this way, correlated components are admitted, but a certain correlation structure is imposed through the choice of the copula. We identify a class of copulae admitting eventually convex chance constraints.

Keywords: Copula; Chance constraints; Log-exp concavity; Probabilistic constraints; Convexity (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4419-9586-5_17

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DOI: 10.1007/978-1-4419-9586-5_17

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