Stochastic monotone wing property: A new dependence structure for copulas

Abstract

In this study, we introduce a novel concept of a copula dependence structure termed the stochastic monotone wing property and investigate its associated properties. This concept is closely related to the monotone conditional variance property, which describes the behavior of the conditional variance of V given U=u as either an increasing or a decreasing function of u for a given random vector (U,V) with a certain distribution function. The need for such a dependence structure arises in various fields, including insurance, where a copula family with the monotone conditional variance property is needed for the joint distribution of frequency and average severity in the collective risk model. Beyond insurance, its applications extend to economics and climatology. Furthermore, this study proposes a new parametric copula family that exhibits the stochastic monotone wing property and provides a method for constructing copulas with this characteristic.