Decomposing Dynamic Risks into Risk Components

The decomposition of dynamic risks a company faces into components associated with various sources of risk, such as financial risks, aggregate economic risks, or industry-specific risk drivers, is of significant relevance in view of risk management and product design, particularly in (life) insurance. Nevertheless, although several decomposition approaches have been proposed, no systematic analysis is available. This paper closes this gap in literature by introducing properties for meaningful risk decompositions and demonstrating that proposed approaches violate at least one of these properties. As an alternative, we propose a novel martingale representation theorem (MRT) decomposition that relies on martingale representation and show that it satisfies all of the properties. We discuss its calculation and present detailed examples illustrating its applicability. This paper was accepted by Baris Ata, stochastic models and simulation.