Few work has analyzed self-protection and self-insurance in relation to multiplicative risks. Occasional treatments highlight differences to additive risk. This paper studies the prevalence, sources, and implications of such differences along various modeling features. Preference conditions differ as soon as mitigation effort or background risk are multiplicative to the foreground risk component in the utility argument. Only models with mitigation cost in utility terms and no background risk show no structural difference. In a numerical example for monetary cost, the same decision maker, who raises loss-risk mitigation with additive background risk, may reduce mitigation with background risk whenever multiplicative risk is present, in the foreground or background.