Risk Allocation and Risk Attribution in Static and Dynamic Settings

Abstract

Risk can be decomposed along two dimensions: risk allocation and risk attribution. On the one hand, the total risk of a company can be allocated to its divisions, using that the company’s profit/loss is the sum of the divisions’ profits/losses. On the other hand, risk is attributed to risk drivers that may affect the company’s profit/loss in a nonlinear way. This thesis deals with risk allocation and risk attribution by extending results from a single-period model to a dynamic setting. For risk allocation, we apply the Euler allocation principle while for risk attribution, we use a linear approximation of the profit/ loss contributions of risk drivers and then apply risk allocation. We also show an example for risk allocation and risk attribution, using the entropic risk measure and simulating the risk drivers in MATLAB.