## Pricing Insurance Risk Course (PIRC)

### Learning Objectives

##### Market and Model Specification

- Define and distinguish assets, capital, surplus, and equity
- Define and compute the return on equity and the cost of capital
- Compute the weighted cost of insurance capital across equity, debt, reinsurance, ILS, and other forms of capital
- Explain what is meant by equal priority in default
- Compute asset allocations given total assets and amounts owed to various parties
- Explain why low volatility risks can be harmed by pooling with high volatility risks
- Explain how to measure whether pooling diversification is effective in a given portfolio

##### Distortions and Spectral Risk Measures

- Define a distortion function and give examples
- Compute loss ratio, leverage and return given a distortion function and return period
- Describe how cat bond prices relate to a distortion function
- 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
- Define the pricing operator associated with a distortion function
- Evaluate the pricing operator on limited and unlimited losses, given a loss distribution function or a sample of equally likely losses
- Describe how properties of a distortion correspond to properties of the associated pricing operator
- Describe the impact of the behavior of a distortion for
*s*=0 and *s*≈1 on implied prices
- 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

- Define technical premium or technical price
- 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
- Distinguish between additive and non-additive pricing models and explain how each handles diversification
- Explain the behavior of traditional and distortion based methods for low and high volatility lines, and with weak and strong capital standards
- 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
- 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