12.3 Independent Risk

Definition 12.2 Independent Risk = Randomness inherent to the insurance process

• Parameter Risk: ability to select correct parameters and appropriate model

• Process Risk: randomness e.g. tossing a die

Use stochastic modeling to analyze independent risk

• Focus on periods where episodes of systemic risk were non-existent or minimal

  Limit the impact of the historical external episodes and allow us to focus on the independent risk

• Supplement with internal and external benchmarking

12.3.1 CoV for Independent Risk

Model the parameter and process risk together

• Mack, bootstrap, stochastic CL, GLM, Bayesian

Ideally the model adequately model away the systemic risk so all that is left is the independent risk

• Residual should only have independent risk

• For small data set: difficult to model away the external systemic risk

  • Solution: Do not model away past episodes of systemic risk

    Use results as starting point and then add a margin for external systemic risks not in data to have a measure of independent and external systemic risk

Complexity of the model should be commensurate with the importance of the total risk margin

Models for outstanding claims liabilities:

• GLM and bootstrapping are particularly useful

• They can isolate the independent risks

• Graphing residuals again AY, age, experience period can used to identify past systemic episodes

Models for premium liabilities:

• GLM, bootstrap, Bayesian

• Can model frequency and severity CoV then combine

  • Frequency: Remove past systemic episodes

  • Severity: Adjust for inflation and seasonality