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Probability & Probability Distributions
Two Important Measures for Probability Distributions
Gross Premium & Risk Charge
How do insurers estimate Expected Losses?
Alternate Probabilities
100
This constant type of probability is based on deductive or basic reasoning rather than actual experience
What is Theoretical Probability
100
The two important measures for probability distributions are?
What is central tendency & dispersion
100
The ________ , or "price" for an insurance contract should cover all costs including claims or losses and administrative costs.
What is gross premium
100
Insurers use ________ to predict future risks.
What is past information
100
________ events cannot occur at the same time and the some of all possible outcomes must equal 1.
What is mutually exclusive
200
The two types of probability distributions are...
What are discrete and continuous
200
The weighted average of all of the possible outcomes of a theoretical probability distribution is referred to as? How is it calculated?
What is Expected Value. The sum of the amount of each loss and the probability of each loss (EV=E XiPi)
200
The ________ is the portion of gross premium needed to pay losses.
What is pure premium.
200
_________ covers situations where insurance not readily available for certain risks and is not covered by standard insurance, such as marijuana growers.
What is excess & surplus market
200
________ occur when one event does not affect the occurrence of any other event. How is it calculated?
What is independent events. P (A "AND"(multiply) B) = P(A) x P(B)
300
______ distributions are typically used as frequency distributions.
What is discrete
300
This "cushion" reflects the estimation risk of the insurer and is dependent on the accuracy and level of confidence in the estimate of EL.
What is risk charge
300
Using the Alamo Car Rental example, what is the expected number of losses (frequency) per auto? (1 of 2 ways) What is the expected number of losses for ALL autos?
A. 1) Col 1 & 3: sum of # of losses per auto per year x probability (# losses) - (0 x .9)+(1 x .08)+(2 x .02) = .12 2) Col 2 & 4: Total # of losses/ # of cars having loss - 120/1000 = .12 B.total # of autos x expected loss (per 1000 cars) - 100000 x .12 = 12,000
300
Two or more events that can occur within a given time period are _______. How are they calculated?
What are non-mutually exclusive events. P (A "OR"(add) B "OR" both) = P (A) + P(B) - P(A "AND" B) P (A OR B but NOT both) = P (A) x P (not B) + P (A) x P (not B)
400
Time, distance, and $ amount of loss are all types of _____
What is continuous distribution
400
The_________ measures variability or dispersion about the mean. How is it calculated?
What is varience. The sum of squared differences between possible outcomes AND the expected value (o^2=E Pi(Xi-EV)^2
400
_____________ such as marketing/advertising, underwriting, and state premium takes may be anywhere from 10-30% of a premium. What is another name for it?
What is administrative costs. Expense Loading
400
Using the Alamo Car Rental example, what is the $ value of losses (severity) for autos with a loss? (1 of 2 ways) What is the expected losses per auto? For all autos?
A. 1) Col 1 & 3: sum of $ amount of lossr x probability ($ losses) - (500 x .25)+(1000 x .5)+(2000 x .25) = $1125 2) Col 2 & 4: Total $ losses/ # of losses - 135,000/120 = $1125 B.expected losses (frequency) x expected loss (severity); EL= E(F) E(S) - 135000/1000 C.avg losses x total # of cars - 135 x 100,000 = 13.5 mil
400
By using this, insurers obtain "accurate" information and reduce risk of adverse outcomes.
What is law of large numbers
500
________ is based on actual data.
What is empirical probability.
500
A firm with a higher ______ has less variation, therefore has less risk. How is it calculated?
What is coefficient of variation. The Standard Deviation (square root of variance) over the mean or expected value (o/u)
500
How is a gross premium calculated?
What is pure premium + risk charge + administrative costs
500
Cases with ___________, such as natural disaster, varies inversely with the level of confidence in expected losses.
What is in the middle information.
500
In _________, such as car insurance the average loss is substituted for the actual loss in order to reduce uncertainty.
What is pooling of losses