Weak Comonotonicity

Forthcoming, European Journal of Operational Research

32 Pages Posted: 28 Dec 2018 Last revised: 13 Sep 2019

See all articles by Ruodu Wang

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Ricardas Zitikis

University of Western Ontario

Date Written: December 12, 2018

Abstract

The classical notion of comonotonicity has played a pivotal role when solving diverse problems in economics, finance, and insurance. In various practical problems, however, this notion of extreme positive dependence structure is overly restrictive and sometimes unrealistic. In the present paper, we put forward a notion of weak comonotonicity, which contains the classical notion of comonotonicity as a special case, and gives rise to necessary and sufficient conditions for a number of optimization problems, such as those arising in portfolio diversification, risk aggregation, and premium calculation. In particular, we show that a combination of weak comonotonicity and weak antimonotonicity with respect to some choices of measures is sufficient for the maximization of Value-at-Risk aggregation, and weak comonotonicity is necessary and sufficient for the Expected Shortfall aggregation. Finally, with the help of weak comonotonicity acting as an intermediate notion of dependence between the extreme cases of no dependence and strong comonotonicity, we give a natural solution to a risk-sharing problem.

Suggested Citation

Wang, Ruodu and Zitikis, Ricardas, Weak Comonotonicity (December 12, 2018). Forthcoming, European Journal of Operational Research, Available at SSRN: https://ssrn.com/abstract=3300276 or http://dx.doi.org/10.2139/ssrn.3300276

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Ricardas Zitikis

University of Western Ontario ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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