This paper investigates how welfare losses for facing risks change as a function of the number of risk exposures. To that aim, we define the risk apportionment of order n (RA-n) utility premium as a measure of pain associated with facing the passage from one risk to a riskier one. Changes in...

This paper extends the concept of precautionary premium to a multivariate setting so as to measure the intensity of the precautionary saving motive to protect against multivariate risks. This makes it possible to disentangle and to link the various motives of precautionary saving depending on...