Wikipedia
In probability theory, comonotonicity mainly refers to the perfect positive dependence between the components of a random vector, essentially saying that they can be represented as increasing functions of a single random variable. In two dimensions it is also possible to consider perfect negative dependence, which is called countermonotonicity.
Comonotonicity is also related to the comonotonic additivity of the Choquet integral.
The concept of comonotonicity has applications in financial risk management and actuarial science, see e.g. and . In particular, the sum of the components is the riskiest if the joint probability distribution of the random vector is comonotonic. Furthermore, the - quantile of the sum equals of the sum of the -quantiles of its components, hence comonotonic random variables are quantile-additive. In practical risk management terms it means that there is minimal (or eventually no) variance reduction from diversification.
For extensions of comonotonicity, see and .