Mango: Risk Load/Game Theory

Question 1

Var(L), Mango

Answer 1

ΣL_i² * p_i * (1 - p_i)

Question 2

Cov(L,n), Mango

Answer 2

Σ[L_i * n_i * p_i * (1 - p_i)]

Question 3

Variance of combined portfolio (L + n)

Answer 3

Var(L) + Var(n) + 2Cov(L,n)

Question 4

Equation for needed surplus

Answer 4

V = z * SD(loss) - expected return

z = number of standard deviations associated with percentile need

Question 5

Risk load, marginal surplus method

Answer 5

Question 6

Risk load, marginal variance method

Answer 6

Question 7

Risk load multiplier, marginal surplus method

Answer 7

yz / (1 + y)

Question 8

Risk load multiplier, marginal variance method

Answer 8

[yz/(1 + y)] / [SD(L + n)]

Question 9

Renewal additivity

Answer 9

The sum of the renewal risk loads is equal to the risk load for the aggregate portfolio

Marginal surplus method: subadditive (square root rule)

Marginal variance method: superadditive (double counts covariance)

Question 10

Covariance Share method

Answer 10

Covariance share = L_X*L_y*2*(L_x / L_X+Y)

Covariance of X = p*(1 - p)*Covariance share

Question 11

Deferred risk load

Answer 11

(Marginal variance risk load - covariance share risk load)