Risk Measures and Capital Allocation Principles for Risk Management

Abstract

Risk measures (or premium principles) and capital allocation principles play a signi cant role in risk management. Regulators and companies in the nancial markets usually adopt an appropriate risk measure, for example, Value-at-Risk (VaR) or Tail Value-at-Risk (TVaR), to determine the benchmarks. However, these risk measures are determined from the loss functions with constant weights, not random weight functions. This thesis proposes new approaches to determine risk measures from two perspectives. Firstly, we will generalize the de nition of the tail subadditivity for distortion risk measures; we de ne the generalized GlueVaR (a linear combination of VaR and TVaRs) to approach any coherent distortion risk measure. Secondly, we will research the risk measures (or premium principles) and capital allocation principles based on the loss functions with random weight functions. The new reinsurance premium principles are derived similarly to the new risk measures. The two thresholds for the weight in the loss function can be employed by reinsurance companies as benchmarks when pricing the reinsurance products. The capital allocation principles derived based on the weighted loss functions are both mathematically and economically reasonable. Many of the risk measures and allocation principles, including the new risk measures, can be covered by this model. The results of this thesis have not only uni ed many of the risk measures and capital allocation principles, but also provided new and practical models.