## Pricing Insurance Risk Course (PIRC)

### Learning Objectives

##### Market and Model Specification
1. Define and distinguish assets, capital, surplus, and equity
2. Define and compute the return on equity and the cost of capital
3. Compute the weighted cost of insurance capital across equity, debt, reinsurance, ILS, and other forms of capital
4. Explain what is meant by equal priority in default
5. Compute asset allocations given total assets and amounts owed to various parties
6. Explain why low volatility risks can be harmed by pooling with high volatility risks
7. Explain how to measure whether pooling diversification is effective in a given portfolio
##### Distortions and Spectral Risk Measures
1. Define a distortion function and give examples
2. Compute loss ratio, leverage and return given a distortion function and return period
3. Describe how cat bond prices relate to a distortion function
4. Plot a distortion function on linear and log scales, and highlight salient features on the plots, including minimum rate on line and suitability as a pricing risk measure
5. Define the pricing operator associated with a distortion function
6. Evaluate the pricing operator on limited and unlimited losses, given a loss distribution function or a sample of equally likely losses
7. Describe how properties of a distortion correspond to properties of the associated pricing operator
8. Describe the impact of the behavior of a distortion for s=0 and s≈1 on implied prices
9. Describe the average of points, convex envelope, bagged convex envelope, and least squares methods of fitting distortions to observed cat bond pricing, and compute the relevant parameters given price data
##### Comparative Pricing
1. Define technical premium or technical price
2. Define and compute technical premiums using a variety of traditional methods and distortion operators, including stand-alone VaR and TVaR, scaled- and equal-risk VaR and TVaR, Merton Perold
3. Distinguish between additive and non-additive pricing models and explain how each handles diversification
4. Explain the behavior of traditional and distortion based methods for low and high volatility lines, and with weak and strong capital standards
5. Explain how target returns vary by line under the distortion model; relate to the cost of various types of capital; describe the implications for reinsurance strategy
6. Explain how negative technical margins can be regarded as appropriate, the situations in which they are most likely to occur, and what their presence means