Universally Marketable Insurance Under Multivariate Mixtures

Abstract

The study of desirable structural properties that define a marketable insurance contract has been a recurring theme in insurance economic theory and practice. In this article, we develop probabilistic and structural characterizations for insurance indemnities that are universally marketable in the sense that they appeal to all policyholders whose risk preferences respect the convex order. We begin with the univariate case where a given policyholder faces a single risk, then extend our results to the case where multiple risks possessing a certain dependence structure coexist. The non-decreasing and 1-Lipschitz condition, in various forms, is shown to be intimately related to the notion of universal marketability. As the highlight of this article, we propose a multivariate mixture model which not only accommodates a host of dependence structures commonly encountered in practice but is also flexible enough to house a rich class of marketable indemnity schedules.

Optimal Reinsurance Design With Distortion Risk Measures and Asymmetric Information

“…More specifically, Cheung et al (2014) define the class of universally marketable indemnities to ensure that the acceptability by policyholders is universal. They show that an indemnity that is assumed to be non-decreasing a priori is universally marketable if and only if it is a 1-Lipschitz function; see also the related discussions in Lo et al (2021). The function f ∈ F is non-decreasing and 1-Lipschitz and hence absolutely continuous.…”

Risk measures induced by efficient insurance contracts

“…More recently, Hofmann et al (2019) studied optimal insurance policy indemnity schedules with limited liability and background risk. Lo et al (2021) analyzed the set of universally marketable indemnities with risk measures preserving convex orders.…”