Risk Aggregation & Capital Allocation: Calibration–Application–Beyond
Risk Aggregation and Capital Allocation: From Calibration to Application and Beyond
Risk diversification is at the heart of insurance. In a modern Enterprise Risk Management (ERM) approach, a company's entire risk profile - including risk diversification and concentration - must be considered in decision-making processes such as insurance pricing, product design, asset allocation and reinsurance. The impact on risk-oriented performance measures such as return on risk-adjusted capital (RORAC) and economic value added (EVA) must also be assessed.
This web session focuses on the aggregation of individual risks to the overall level of an insurance company. To achieve this, we apply both deterministic and stochastic copula-based approaches, along with key risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). The outcome of this process is the capital requirement, which must be covered by the company’s own funds—a limited and costly resource that necessitates careful management.
Against this backdrop, we explore risk steering methods that support economically sound decision-making, addressing key questions such as:
- How can we impose effective risk limits for business segments?
- How can we identify value-enhancing and value-reducing business segments in the context of the firm’s overall risk profile?
- How can we make informed decisions on risk mitigation tools?
- How can we incorporate the cost of capital into insurance pricing?
A fundamental concept underlying all these questions is capital allocation, and specifically the gradient (Euler) capital allocation principle. The principle is directly linked to “marginal capital requirements” and is compatible with the performance measures mentioned above.
However, the proper implementation of capital allocation in risk management, risk limiting, and decision making often imposes significant challenges. On the computational side, the gradient allocation principle requires determining the derivative of the risk measure—typically Value-at-Risk or Expected Shortfall—with respect to business volumes or other decision variables. Obtaining these derivatives is numerically challenging, especially when risk measurement relies on Monte Carlo simulations. We demonstrate methods to enhance the stability of these estimations, such as kernel estimation. In addition, the allocation has the limitation of accounting only for the risk diversification effects of the current portfolio, which can easily become invalid if the portfolio changes and new risk concentration and diversification patterns emerge. To tackle this issue, we present a recently developed methodology called "Orthogonal Convexity Scenarios" (OCS), which helps to proactively identify potentially adverse portfolio shifts and integrate them into risk management and business steering.
