Methods and Applications of Analysis

Volume 18 (2011)

Number 3

Lebesgue property of convex risk measures for bounded Càdlàg processes

Pages: 335 – 350



Hirbod Assa (Department of Mathematics and Statistics, University of Montreal, Quebec, Canada)


In this paper, we study the Lebesgue property for convex risk measures on the class of bounded Càdlàg processes. For that, we characterize the compact subsets of a family of bounded variation processes, which is, of course, the topological dual of the bounded Càdlàg processes, in an appropriate topology. We show that the Lebesgue property can be characterized in several equivalent ways.


convex risk measures, bounded Càdlàg processes, Lebesgue property, static risk

2010 Mathematics Subject Classification

46A20, 52A07, 60G07, 91B16, 91B30

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