1. Managing Underwriting Risk & Capital
John J. Kollar, FCAS, MAAA, CPCU
July 30, 2003

2. Enterprise Risk Management
Investment Risk
Underwriting Risk
Catastrophe
Risk

3. Underwriting Risk Loss volatility (including catastrophic risk)
Correlation between lines (dependencies)
Risk of adverse development for long-tailed lines
Underwriting cycles=varying margins
Varying real prices
Varying underwriting selectivity

4. Constructing an Underwriting Risk Model (URM)
Fit claim severity distributions by line.
Use individual claim severity
Aggregate data of many insurers
By line
By settlement lag
to estimate industry parameters for claim severity distributions

5. Constructing URM (Cont’d)
Fit claim frequency distributions by line.
Use net expected losses, exposures
By insurer
By line
By settlement lag
To estimate
Industry parameters for the claim frequency distributions
Correlations between lines

6. URM Input Insurer expected losses Policy Limits Reinsurance
By line
By settlement lag
Policy Limits
Reinsurance
Use industry estimates for other parameters.
Include insurer’s catastrophe loss distributions (catastrophe modeler).
Can adjust losses by an economic
scenario generator.

7. Calculating an Insurer’s Underwriting Risk Via URM
Use the collective risk model.
Separate claim frequency and severity analysis.
For each line of insurance:
Select a random claim count.
 Use industry claim frequency parameters.
Select random claim size for each claim.
 Use industry claim severity parameters.
 Adjust for policy limits and reinsurance.

8. Calculating an Insurer’s Underwriting Risk Via URM (Cont’d)
The aggregate loss for all lines = sum of all the random claim amounts for all lines.
Reflect the correlation between lines of insurance.
Repeat the above thousands of times (simulation) or use Fourier transforms to calculate the insurer’s aggregate loss distribution.
Total
By profit center

9. Calculating an Insurer’s Underwriting Risk Via URM (Cont’d)
What is the tolerance for risk?
Regulatory requirement (RBC)
“A” rating from a rating agency
Tradition, etc.
Select a statistical measure of risk that corresponds to the tolerance for risk.
Value at risk
Tail value at risk
Standard deviation, etc.
Determine total capital for underwriting from the aggregate loss distribution using the selected measure of risk.

10. Allocating (Cost of) Capital
Calculate marginal capital for each profit center.
Calculate the sum of the marginal capital for all capital centers.
Diversification multiplier equals the total capital divided by the sum of the marginal capital.
Allocated capital for each profit center equals the product of the diversification multiplier and the marginal capital for the profit center.

11. Minimizing the Cost of Financing
Cost of capital = return x capital
Discounted
Post tax
By profit center
Cost of reinsurance = frictional cost
For each program
Cost of financing = cost of reinsurance + cost of capital
For each program/profit center
Minimize the total cost of financing

12. Setting Combined Ratio Targets by Line
Expected losses
Expected expenses
Investment income
Cost of financing

13. Planning Underwriting Strategy
Add policies/portfolios that increase the return on capital.
Drop policies that cause a drop in return on capital.