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20 Cards in this Set
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 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 

Variance

 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 

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 

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  689599 

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? 
 selfinsurance!  large employers often use pooling to selfinsure some of their areas of risk like workers' comp and employersponsored health insurance 