Some new notions of dependence with applications in optimal allocation problems

Jun Cai, Wei Wei

Research output: Contribution to journalArticlepeer-review


Dependence structures of multiple risks play an important role in optimal allocation problems for insurance, quantitative risk management, and finance. However, in many existing studies on these problems, risks or losses are often assumed to be independent or comonotonic or exchangeable. In this paper, we propose several new notions of dependence to model dependent risks and give their characterizations through the probability measures or distributions of the risks or through the expectations of the transformed risks. These characterizations are related to the properties of arrangement increasing functions and the proposed notions of dependence incorporate many typical dependence structures studied in the literature for optimal allocation problems. We also develop the properties of these dependence structures. We illustrate the applications of these notions in the optimal allocation problems of deductibles and policy limits and in capital reserves problems. These applications extend many existing researches to more general dependent risks.

Original languageEnglish (US)
Pages (from-to)200-209
Number of pages10
JournalInsurance: Mathematics and Economics
Issue number1
StatePublished - Mar 2014
Externally publishedYes


  • Arrangement increasing
  • Capital reserve
  • Comonotonicity
  • Copula
  • Deductible
  • Dependence notion
  • Optimal allocation
  • Policy limit
  • SAI
  • Stochastic order
  • UOAI

ASJC Scopus subject areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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