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Topic 4. Quantitative Methods

Topic 4. Quantitative Methods. BUS 200 Introduction to Risk Management and Insurance Jin Park. Overview. Terminology Application in Risk Management & Insurance Insurance Premium Using Probabilistic Approach. Terminology. Probability The likelihood of an event

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Topic 4. Quantitative Methods

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  1. Topic 4. Quantitative Methods BUS 200 Introduction to Risk Management and Insurance Jin Park

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

  3. Terminology • Probability • The likelihood of an event • The relative frequency of an event in the long run • Range 0 to 1, inclusive • Non-negative

  4. Terminology • Probability • Theoretical, priori probability • Number of possible equally likely occurrences divided by all occurrences. • Historical, empirical, posteriori probability • Number of times an event has occurred divided all possible times it could have occurred. • Not a true probability • Subjective probability • Professional or trade skills and education • Experience • Random variable (or r.v.) • A number (or numeric outcome) whose value depends on some chance event or events

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

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

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

  8. Examples Loss Distribution Expected Loss, Mean Standard Deviation = 1.6271 Variance Coefficient of Variation = 3.62

  9. Which one faces more risk? • Probability Distribution for the # of robbery per month for Store A and B

  10. Decision • Store B faces more risk because the higher measure of variance or the standard deviation. • Another case

  11. Probability Distribution

  12. Application in RMI • Loss Frequency • Loss Severity • Maximum possible loss • Maximum probable loss • Loss Frequency Distribution • Loss Severity Distribution • Total Loss Distribution

  13. Application in RMI • Maximum possible loss • 10,000 • Independent of probability • Maximum probable loss • 98% chance that losses will be at most $5,000 • 95% chance that loss will be at most $1,000

  14. Application in RMI - Frequency A rental company with 1,000 rental cars Expected # of accidents per auto (frequency) = Expected total # of losses = 120

  15. Application in RMI – Severity • Case 1 - Severity per accident is not random. • Let severity = $1,125 1. What is expected $ loss per auto? • $1,125 x 0.12 = $135 2. What is expected $ loss for the rental company in a given time period? • $135 x 1,000 cars = $135,000

  16. Application in RMI • Case 2 - Severity is random with the following distribution. • What is expected $ loss per accident? $1,125 • What is expected $ loss per auto? $135

  17. Insurance Premium • Gross premium • premium charged by an insurer for a particular loss exposure = pure premium + risk charge + other loadings • Pure premium = Expected Loss (EL) • A portion of the gross premium which is calculated as being sufficient to pay for losses only. • Pure premium must be estimated.

  18. Insurance Premium • Risk Charge (Risk Loading) • To deal with the fact that EL must be estimated, and the risk charge covers the risk that actual outcome will be higher than expected • 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 • Example: • Risk charge for terrorism coverage would be _______. • Risk charge for personal automobile insurance would be _______.

  19. Insurance Premium • Other Loadings • Expense loading • Administrative expenses, including advertising, underwriting, claims, general expenses, agent’s commission, etc … • Profit loading

  20. Insurance Premium • Expected Loss (frequency) • 0.06 loss/exposure • Expected $ Loss (severity) • $2,500 per loss • Risk charge - 10% of pure premium • Profit loading – 5% of pure premium • Expense loading - $60 • Gross premium =

  21. Insurance Premium Risk Charge = 495/450 = 10%

  22. Using Probabilistic Approach Simple example of event tree What is the expected severity of a fire? $19,990

  23. Using Probabilistic Approach What if there is no sprinkler system… What is the expected severity of a fire? $1,009,000

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