This paper presents a new axiomatic characterization of risk measures that are additive for independent random variables. In contrast to previous work, we include an axiom that guarantees monotonicity of the risk measure. Furthermore, the axiom of additivity for independent random variables is...

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 of insurance risks focusing in...