Formulas

Question 1

Is VaR is a coherent risk measure? If not, which properties does it not satisfy?

Answer 1

No, subbaditivity

Question 2

Is TVaR is a coherent risk measure? If not, which properties does it not satisfy?

Answer 2

Yes

Question 3

Define that probability generating function

Answer 3

Px(t) = E(t^x)

Question 4

What is the formula for U for confidence intervals of S(x) and H(x)?

Answer 4

Define formula

Question 5

Describe the difference between Buhlmann and Bayes estimates

Answer 5

• Buhlmann is least squares approximation to Bayesian
• Buhlmann always form a linear function and cannot be entirely or below the Bayesian estimate
• Bayesian estimates may not fall outside of the hypothetical means, but the Buhlmann estimates can

Question 6

Partial credibility formulas:

• Limited fluctuation
• Buhlmann’s credibility

Answer 6

Define formula

Question 7

Define the conjugate priors and their predictive models

Answer 7

• Poisson/Gamma
• Normal/Normal
• Bernoulli/Beta
• Exponential/Inverse Gamma

Question 8

Define the formulas for the Polar simulation method

Answer 8

u1 and u2

Question 9

Exposure and coverage modifications for Poisson, Binomial, NB

Answer 9

Poisson, Binomial, NB`

Question 10

Formulas for Normal and Lognormal VaR and TVaR

Answer 10

Define formula

Question 11

Define ej, qj and Var(qj) for the exact exposure method

Answer 11

Define formula

Question 12

Define ej, qj and Var(qj) for the actuarial exposure method

Answer 12

Define formula

Question 13

What is the formula for a D(x) plot

Answer 13

D(x) = Fn(x) - F(x*)

Question 14

What is the formula for a p-p plot

Answer 14

i/(n+1) on x axis and fitted distribution on y

Question 15

What is the formula for Chi-Square

Answer 15

Define formula