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Notes Topic 4 Quantitative Methods Quantifying Frequency and Severity and Risk Management Applications Risk Variability o Variation of Actual Loss around Expected Loss o Measuring Expected Loss Dollars o Measuring Variability P o P Single Exposure Unit o P Group of Similar Exposure Units EXAMPLE Exposure Unit Item Person or Thing of value that is exposed to loss Property Life Insurance Reputation Car Accidents X amount of loss over a given time X Example of random variable Possible values for losses Probability Loss Amount in Will be provided 0 85 1 000 Occurs 10 Of The Time 5 000 3 10 000 2 100 Expected Loss P 0 0 85 1 000 0 10 5 000 0 03 10 000 0 02 450 No Actual Loss Group of similarly situated drivers will average 450 Single Exposure 1 Driver with 14 years driving experience 1st 13 years No Accidents 14th year 1 Accident that cost 80 000 0 0 0 0 0 0 0 0 0 0 0 0 0 80 000 1 Sum of All Losses 80 000 5 714 Number of Years 14 EXAMPLE 2 EXAMPLE 3 86 Drivers in a fleet 2013 No accidents for 72 drivers 14 drivers had accidents for total losses of 63 620 63 620 740 per driver 86 Basis For Insurance Company Pricing Gross Premium Premium paid per unit of coverage to insure a particular risk Coverage should be sufficient to cover all costs But claim is settled Once the claim is settled you cant go back signed for full and final settlement Costs are built into Insurance contract insurer doesn t know all of the costs until the o Claims Losses o Administrative Costs Gross Premium Pure Premium Risk Charge Administrative Costs o Pure Premium Pays for LOSSES only o Risk Charge Cushion Buffer that represents estimate of risk Because they don t know what to charge you What Influences Risk Charge Prior Losses and experiences Basis for Risk Charge No Prior experience Knowledge in new job Not going to take a chance that could lead to the premium increasing o Applies to Auto Insurance Life Insurance Health Insurance o Administrative Costs Insurance Company expenses Especially for employees such as Benefits Wages Salaries Mortgage Rent Advertising Premium Tax runs from 10 30 Rules of Probability Measuring Likelihood of an event o Chances or Odds o 0 Impossible o 1 Certain EXAMPLE o Transportation Companies A B and C All products shipped same way Multiply o Compound Joint Outcome But sometimes shipments get stolen Probability of any single shipment being stolen 10 10 was given to us by professor Probability of shipment A B will be stolen P A is Stolen P B is Stolen 10 10 1 other Individual Probability 1 o Mutually Exclusive CANNOT Occur at same time Coin cant be heads tails must be one or Send Shipment A It arrives or it doesn t It cannot arrive and not arrive at the same time Arrives Doesn t Arrive ADD P A is Stolen P A is NOT Stolen 10 NOT Stolen P A is 10 10 1 o P A is NOT Stolen 1 10 90 Statistics My Guess and How Good Is It o Life consists of lies damned lies and statistics Number to support any conclusion o Finding the right Information How You Present It Very Important Key Law of Large Numbers o Over time the more data you collect more observations that occur your results will get closer to accurate results Max Possible Loss Objective Max Probable Loss Subjective o Loss Amount Probability 0 0 85 85 1 000 0 10 10 5 000 0 03 3 10 000 0 02 2 Loss will be 1 000 or less 95 Add Probability 0 85 0 10 Chance of 5 000 or less 98 Add Probability 0 85 0 10 0 03 Max Possible Loss Max Probable Loss Key How You Present in 10 000 Possibility of that happening 2 Subjective But is largest loss that most likely will occur P Expected Loss Calculating Expected Loss o EXAMPLE Enterprise Rent A Car Gives us 1 000 cars fleet 1 Determine Frequency of Loss 2 Calculate Expected Number of Accidents 3 Determine Severity Loss Amount in 4 Measure Total Loss Exposure To Answer Ultimate Question o How Much Will It Cost 1 000 Of Accidents per Driver of Drivers With Losses of Accidents 0 1 2 900 80 20 0 80 40 Probability 0 0 08 8 0 04 4 Above Professor described as a Frequency 900 1000 90 80 1000 8 Total of Accidents 120 20 1000 2 Total of Drivers 1 000 0 12 12 Severity When Losses Occur Loss 1 500 Frequency Severity Expected Loss o 0 12 1 500 180 per auto 0 12 or 12 was brought down from above o 180 1 000 180 000 for 120 accidents New Numbers Below Given By Professor 500 30 to fix 1 000 60 to fix 2 000 30 to fix Total Loss 30 500 60 1 000 30 2 000 135 000 Total Loss in 135 000 1 125 per auto Total 120 Frequency 12 1 125 135 per auto 135 1 000 Expected Loss Whole Fleet 135 000

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