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20 Cards in this Set

  • Front
  • Back

mean frequency and severity of losses

- informed estimates of likely impact of losses in budget year

- employ basic statistical concepts b/c losses are RVs in making estimates

- most types of loss experience fit normal distribution

Random Variables

- future value is not known with certainty

Probability Distributions

- based on empirical or priori data

- shows all possible outcomes for RV, as well as probabilities of occurring

- if don't know prob. distribution, must estimate, often from prior experience or industry data

Expected Value

- frequency times severity

- expected financial outcome associated with each firm's exposures to risk

- sum of multiplication of each possible outcome (expected loss) of the variables with its probability

- starting point for calculating insurance premium or how much firm should set aside each year to cover losses

- measure of long run loss that should be expected


- degree to which actual losses from loss distribution deviate from expected loss; used to calculate margin of error around estimates of expected losses

- how outcomes of RVS vary around expected value of that variable

- not measured in original unit of currency we used to measure loss

Steps to calculate variance

- find expected value (or expected loss)

- Subtract expected loss from each possible outcome, square differences, multiply each by probability of occurring and sum all products together

Standard deviation

- degree to which actual losses from loss distribution deviate from expected loss; used to calculate margin of error around estimates of expected losses

- square root of variance, but expressed in same units as data

Loss frequency

- discrete

- average number of losses

- example: total number of accidents divided by total units analyzed

Loss Severity

- continuous

- average size of loss

- example: total amount of losses divided by total number of accidents

Average loss

- average loss frequency multiplied by average loss severity


- construct loss distribution by calculating all possible combos of losses indicated by frequency and severity loss distributions, as well as their corresponding probabilities of occurring

- often done by computer simulation due to complexity of calculations

Risk Pooling

- ability to reduce each exposure unit's risk by making more accurate predictions about large pool of units

- probability of largest loss is reduced

- minimizes risk and premium charges

How to reduce risk using risk pooling

- if pool members have homogeneous risks, then all members have same expected loss individually, but risk reduction is achieved

- increased size of risk pool reduces risk (STD decreases with increased pool members)

- relationship between risk and pool size- unpooled STD/ SQRT # of pool members

- sort consumers into homogeneous categories, yet still independent of each other

Normal Probability Distribution (Bell Curve)

- Large n, smaller STD- better calculation of premium b/c increased chance that loss will fall near mean loss, compared to smaller n, which could result in miscalculation

- 68-95-99

Confidence Interval

- tells us the uncertainty around loss projections

- Estimated mean loss +/- (k)*Estimated STD

- typically focus on the upper tail to make sure we have enough to fund loss if ends up being larger than estimated mean loss

- decreases with large N and small STD

Estimated mean loss +/- (k)*Estimated STD

- est. mean loss- calculated using data from previous years

- k- specified number of standard deviations which reflect uncertainty resulting from forecasting losses

- STD- calculated using loss data from past

Risk Charge

- (k) * Est. STD- representing margin of error that arises from estimating unknown variable

How to reduce risk

- through diversification

- through risk pooling

What are typical reasons why insurers will not insure?

- when exposure units small, and have insufficient data to forecast losses

- when losses not independently distributed, and can financially ruin insurer, or when affects too much of population at once

Who can use risk pooling other than insurance companies?

- self-insurance!

- large employers often use pooling to self-insure some of their areas of risk like workers' comp and employer-sponsored health insurance