Managing
Underwriting Risk
& Capital
John J. Kollar, FCAS, MAAA, CPCU
July 30, 2003
Enterprise Risk Management
Enterprise Risk
Investment Risk
Underwriting Risk
Catastrophe
Risk
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
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
– By line
– By settlement lag
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
– By line
– By settlement lag
• Correlations between lines
URM Input
• Insurer expected losses
– 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.
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.
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
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.
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.
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
Setting Combined Ratio Targets
by Line
•
•
•
•
Expected losses
Expected expenses
Investment income
Cost of financing
Planning Underwriting Strategy
• Add policies/portfolios that increase the
return on capital.
• Drop policies that cause a drop in return
on capital.