Improved convex upper bound via conditional comonotonicity

Comonotonicity provides a convenient convex upper bound for a sum of random variables with arbitrary dependence structure. Improved convex upper bound was introduced via conditioning by Kaas et al. [Kaas, R., Dhaene, J., Goovaerts, M., 2000. Upper and lower bounds for sums of random variables. Insurance: Math. Econ. 27, 151–168]. In this paper, we unify these results in a more general context using the concept of conditional comonotonicity. We also construct an approximating sequence of convex upper bounds with nice convergence properties.