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