On the Capital Allocation Problem for a New Coherent Risk Measure in Collective Risk Theory

Abstract

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. We focus our motivation and discussion on the problem of capital allocation. Indeed, this risk measure is well-suited to address the problem of capital allocation in an insurance context. We show that the capital allocation problem for this risk measure has a unique solution determined by the Euler allocation method. Some examples and connections with existing results as well as practical implications are also discussed.

Keywords

• capital allocation
• Euler allocation method
• coherent risk measures
• Lévy insurance processes
• risk measures on the space of stochastic processes