In this paper we introduce a new coherent cumulative risk measure on a subclass in
the space of càdlàg processes. This new coherent risk measure turns out to be tractable enough within a class of models where the aggregate claims is driven by a spectrally positive Lévy process. Moreover, this risk measure is well-suited to address the problem of capital allocation in an insurance context. Indeed, we show that the capital allocation problem for this risk measure has a unique solution determ
ined by the Euler allocation method. Some examples are provided.