Ch 2 probability and statistics fin 3040
Hard market: Insurance companies _______ their premiums
Raise
Soft market and hard market example
Soft market example: Life insurance Hard market example: Director's and officer's liability insurance
For a binomial distribution, the standard deviation is:
Square root of n x p x q
CV=
Standard deviation/x bar or mean
Underwriting risk
# of units insured x standard error of the avg. loss distribution
The standard deviation of a distribution is a measure of
Risk or dispersion.
X bar=
Sum of xipi
Amount of loss=
Xi
Normal probability distribution
- More realistic - More useful - Can be employed in more situations
Normal distributions
- More versatile - More realistic - Small number exposures
Binomial distributions
- Require discrete variables (loss or no loss) - Small number exposures
Mean
Nxp
Expected probability of loss=
Pi
Poisson distributions
- Use if exposure units are over 50 and probability of loss is very small
Q=
1-p
Normal probability distribution range of std dev
68% of all losses will be within 1 std dev of the mean 95% of all losses will be within 2 std dev of the mean 99% of all losses will be within 3 std dev of the mean
Soft market: Insurance companies ________ their premiums
Lower
The higher the standard deviation, the _________ the uncertainty loss
Greater
9/11 resulted in a hard or soft market?
Hard: Large losses and bad investment returns
Example of nonrenew after 60 days
Homeowner's insurance after a hurricane
Soft markets are more ______ in their underwriting
Liberal
Binomial distribution: What outcomes exist
Loss or no loss
Central Limit Theorem
The distribution of the sample mean will approach the normal distribution as the sample size increases
Underwriting risk=
n x std dev of x bar or square root of n x std dev of x n= # of units insured std dev x bar= standard error of a distribution std dev x= standard deviation of losses