  Random shifting typically appears in credibility models whereas random
scaling is often encountered in stochastic models for claim sizes reflecting
the time-value property of money. In this article we discuss some aspects of
random shifting and random scaling in insurance focusing in particular on
credibility models, dependence structure of claim sizes in collective risk
models, and extreme value models for the joint dependence of large losses. We
show that specifying certain actuarial models using random shifting or scaling
has some advantages for both theoretical treatments and practical applications.
