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4. Quantitative Methods & Applications

4. Quantitative Methods & Applications. BUS 200 Introduction to Risk Management and Insurance Fall 2008 Jin Park. Overview. Probability Distribution Application in Risk Management & Insurance Insurance Premium Using Probabilistic Approach.

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4. Quantitative Methods & Applications

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  1. 4. Quantitative Methods & Applications BUS 200 Introduction to Risk Management and Insurance Fall 2008 Jin Park

  2. Overview • Probability Distribution • Application in Risk Management & Insurance • Insurance Premium • Using Probabilistic Approach

  3. Representations of all possible events along with their associated probabilities Example; Total number of points rolled with a pair of dice. Probability Distribution

  4. Different Events • Mutually exclusive (events) • The probability of two mutually exclusive events occurring at the same time is ____ . • Collectively exhaustive (events) • Independent (events)

  5. Probability Distribution • Measure of central tendency • Mean, Median, Mode • Measure of variability (risk) • Difference (Min, Max) • Variance • Standard deviation • Coefficient of variation • “Unitless” measure

  6. Probability Distribution

  7. Exercise 1 • Article: Mom wins dream house • Number of tickets • Chances of winning • Price of a ticket • Total proceeds • Total payouts

  8. Exercise 2 • Article: Cadillac Escalade tops with car thieves. • Severity per insured Escalade • Theft frequency • Severity per theft

  9. Insurance Premium • Gross premium = Pure premium + Risk charge + Other loadings • Pure premium = Expected Loss (EL) = Expected Frequency x Expected Severity • Estimated amount to pay for expected loss. • Risk charge (Risk loading) • Amount to cover the risk that actual loss may be higher than expected loss • Other Loadings • Expenses and profits

  10. Risk Charge (Risk Loading) • What determines the size/magnitude of the risk charge? • Amount of available past information to estimate EL • The level of confidence in the estimated EL. • The higher the level of confidence in the estimated EL, the _____ the risk charge. • The number of loss exposures insured by the insurer • The size of loss exposures • Risk charge for terrorism coverage would be _______ than that for personal automobile insurance.

  11. Probabilistic Risk Analysis Simple example of event tree What is the expected severity of a fire? $19,990

  12. Probabilistic Risk Analysis What if there is no sprinkler system… What is the expected severity of a fire? $1,009,000

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