Jae Youn Ahn

Negative dependence concept in copulas and the marginal free herd behavior index

We provide a set of copulas that can be interpreted as having the negative extreme dependence. This set of copulas is interesting because it coincides with countermonotonic copula for a bivariate case, and more importantly, is shown to be minimal in concordance ordering in the sense that no copula exists which is strictly smaller than the given copula outside the proposed copula set. Admitting the absence of the minimum copula in multivariate dimensions greater than 2, the study of the set of minimal copulas can be important in the investigation of various optimization problems. To demonstrate the importance of the proposed copula set, we provide the variance minimization problem of the aggregated sum with arbitrarily given uniform marginals. As a financial/actuarial application of these copulas, we define a new herd behavior index using weighted Spearmans rho, and determine the sharp lower bound of the index using the proposed set of copulas.

Multivariate countermonotonicity and the minimal copulas

FrchetHoeffding upper and lower bounds play an important role in various bivariate optimization problems because they are the maximum and minimum of bivariate copulas in concordance order, respectively. However, while the FrchetHoeffding upper bound is the maximum of any multivariate copulas, there is no minimum copula available for dimensions d3. Therefore, multivariate minimization problems with respect to a copula are not straightforward as the corresponding maximization problems. When the minimum copula is absent, minimal copulas are useful for multivariate minimization problems. We illustrate the motivation of generalizing the joint mixability to d-countermonotonicity defined in Lee and Ahn (2014) through variance minimization problems and show that d-countermonotonic copulas are minimal copulas.

Measuring herd behavior: properties and pitfalls

Abstract Herd behavior is an important economic phenomenon, especially in the context of the recent financial crises. Prior studies propose several measures to quantify herd behavior. In this paper, we show that these measures reflect different perspectives on this behavior, and hence, their interpretation requires great care. Taking a critical attitude toward existing herd behavior measures, we study their properties and pitfalls in detail.