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20 Cards in this Set
- Front
- Back
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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 |
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Random Variables
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- future value is not known with certainty
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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
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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 |
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Variance
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- 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 |
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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 |
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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
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Loss frequency |
- discrete - average number of losses - example: total number of accidents divided by total units analyzed |
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Loss Severity |
- continuous - average size of loss - example: total amount of losses divided by total number of accidents |
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Average loss |
- average loss frequency multiplied by average loss severity |
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Convolution |
- 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 |
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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 |
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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
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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 |
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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
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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 |
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Risk Charge |
- (k) * Est. STD- representing margin of error that arises from estimating unknown variable |
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How to reduce risk |
- through diversification - through risk pooling |
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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
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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 |
