Risk reducers in convex order

Abstract

Given a risk position X, a random addition Z is called a risk reducer for X if the new position X + Z is less risky than X + E[Z] in convex order. We utilize the concept of convex hull to give a structural description of risk reducers in the case of an atomless probability space. Then we study risk reducers that are fully dependent on X. Applications to multivariate stochastic ordering, index-linked hedging strategies, and optimal reinsurance are proposed.

Universally Marketable Insurance Under Multivariate Mixtures

“…As far as the authors are aware, the intimate connections between the nondecreasing and 1-Lipschitz condition and the marketability of indemnities were first formally brought out only recently in Cheung et al (2014) as a natural application of the concept of risk reducers (see also a further study of risk reducers in He et al (2016)). In a standard expected utility setting, Cheung et al (2014) introduced a class of indemnities which are acceptable to all policyholders in the sense that it is always possible to price the indemnity in such a way to raise the expected utility of any given policyholder as well as to cover the expected cost of the insurer.…”