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General convex order on risk aggregation

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  • Edgars Jakobsons
  • Xiaoying Han
  • Ruodu Wang

Abstract

Using a general notion of convex order, we derive general lower bounds for risk measures of aggregated positions under dependence uncertainty, and this in arbitrary dimensions and for heterogeneous models. We also prove sharpness of the bounds obtained when each marginal distribution has a decreasing density. The main result answers a long-standing open question and yields an insight in optimal dependence structures. A numerical algorithm provides bounds for quantities of interest in risk management. Furthermore, our numerical results suggest that the bounds obtained in this paper are generally sharp for a broader class of models.

Suggested Citation

  • Edgars Jakobsons & Xiaoying Han & Ruodu Wang, 2016. "General convex order on risk aggregation," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2016(8), pages 713-740, September.
    • Handle: RePEc:taf:sactxx:v:2016:y:2016:i:8:p:713-740
    DOI: 10.1080/03461238.2015.1012223
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