Guo, Qiheng, Daniel Bauer, and George H. Zanjani. 2021. “Capital Allocation Techniques: Review and Comparison.” Variance 14 (2).
• Figure 1. Overview of capital allocation methods
• Table 1. Implementation of allocation methods
• Table 2. Conventional allocation results, heterogeneous Bernoulli case
• Figure 2. Comparison of allocations, heterogeneous Bernoulli losses, groups of 5 consumers—(a) and (b) are details of main graph
• Figure 3. Histogram of aggregate loss from a catastrophe reinsurance company
• Table 3. Descriptive statistics of all 24 lines
• Table 4. Descriptive statistics of four aggregated lines
• Figure 4. Histograms of four aggregated lines from a catastrophe reinsurance company
• Table 5. Conventional allocation results, catastrophe reinsurance case
• Table 6. Profit loadings on expected losses as pricing result using calibrated risk measures
• Figure 5. Stability of allocations: Distance between allocations on basic and modified portfolios for all methods
• Figure 6. Stability of allocations: Distance between allocations on basic and modified portfolios for allocation methods (except Exp and VaR)
• Appendix B. Additional tables and figures

Table 7. Optimization and allocation results: Bauer-Zanjani allocation, heterogeneous Bernoulli losses
• Table 8. Optimization and allocation results: Bauer-Zanjani allocation, catastrophe reinsurance losses
• Figure 7. Comparison of allocations, catastrophe insurance losses

Abstract

Capital allocation is an essential task for risk pricing and performance measurement of insurance business lines. This paper provides a survey of existing capital allocation methods, including common approaches based on the gradients of risk measures and economic allocation arising from counterparty risk aversion. We implement all methods in two example settings: binomial losses and loss realizations from a catastrophe reinsurer. We assess stability based on sensitivity analysis with regard to losses. Our results show that capital allocations appear to be intrinsically (geometrically) related, although the stability varies considerably. We find stark differences between common and “economic” capital allocations.

This paper was funded through Casualty Actuarial Society sponsored research on “Allocation of Costs of Holding Capital”.

Accepted: February 15, 2020 EDT