Chapter 2: Apendix Flashcards
How to compute expected value?
Loss %1 * Amount of Loss 1 + Loss %2 * Amount of loss 2โฆ.
What does standard deviation mean in regards to uncertainty of loss?
The greater the standard deviation, the greater uncertainty of loss.
How to calculate standard deviation?
(Amount of Loss1 - Amount of Loss 1)^2 (Probability of Loss1) + (Amount of Loss2 - Amount of Loss2)^2 (Probability of Loss2)โฆ..= variance, Sqrt = SD
What does the central limit theorem state?
The distribution of the sample mean will approach the normal distribution as the sample size increases
What are the three probability distributions?
- Binomial
- Normal
- Poisson
When do you use the binomial probability distribution?
- Requires discrete variables (loss or no loss)
- Small number exposures
When do you use the normal probability distribution?
- Normal
- More versatile
- More realistic
- Small number exposures
When do you use the poisson probability distribution?
Use if exposure units are over 50 and probability of loss is very small
In a normal probability distribution losses are arranged as:
- 68% of all losses will be within 1 standard deviation of the mean
- 95% of all losses will be within 2 standard deviations of the mean
- 99% of all losses will be within 3 standard deviations of the mean
In binomial distribution what outcomes exist?
Loss or no loss
How to calculate mean for binomial distribution?
n x p = mean
What does the standard deviation of a binomial distribution measure?
risk or dispersion. For a binomial distribution, the standard deviation is, calculated by SQRT of N X P X Q
What is underwriting risk?
When an insurance company increases the size of the sample insured, underwriting risk (maximum insured loss) increase because more insured exposure units could suffer a loss.
How to calculate underwriting risk?
- Underwriting Risk = # of units insured x standard error of the avg. loss distribution
- n x ๐๐ฅ or โ๐x ๐x
n = # of units insured
๐๐ฅ = standard error of a distribution
๐๐ฅ = standard deviation of losses
In a hard market how do underwriters act?
- Insurance companies raise their premiums or less coverage for the same premium
- More โconservativeโ in their underwriting
- Restricted contract provisions
- September 11 resulted in a hard market (large losses & bad investment returns