RMIN 5950 quiz 3 lectures 6 & 7

Quantitative Methods in Risk Management

- Probability - definition and rules - Statistical measures - Loss distributions - Law of large numbers - Regression (loss forecasting)

Probability

- Proportion of losses among a large number of exposures - Proportion of losses over a long period - Time v. exposures

Measures of location

- mean ( μ ) - median - mode

Statistical Measures

- measures of location - measures of dispersion

Measures of dispersion

- range - variance / standard deviation (σ) - coefficient of variation (σ/μ)

Confidence Bounds

Based on empirical distribution - P( X>900 ) = .1 Normal distribution assumption - =1-NORMDIST (900,460,309.84,TRUE) - P( X>900 ) = .078 Other theoretical distributions

Probability Rules

Mutually exclusive P(A ∩ B) = 0 Independence P(A ∩ B) = P(A)•P(B) Conditional probability example: P(E) = .01, P(F) = .10, P(E ∩ F) = .009 P(F | E) = ? P(E ∩ F)/P(E) = .009/.01 = .90

Probability Distributions

Number of occurrences - frequency distribution Severity of losses - severity distribution - conditional distribution Total $ losses in a given period - total claims distribution