Brosius

Question 1

Advantage of Least Squares method

Answer 1

flexibility to include link ratio and budgeted loss methods as special cases

Question 2

Disadvantages of Least Squares methodology (2)

Answer 2

1. sampling error can lead to values of a and b that don’t make sense
2. significantly impacted by systematic changes in loss experience and must be adjusted before using

Question 3

Best use for Least Squares methodology

Answer 3

significant random fluctuations

Question 4

Least Squares formulas (3)

Answer 4

L(x) = a + bx
b = [ avg(xy) - avg(x) * avg(y) ] / [ avg(x^2) - avg(x) ^2 ]

Question 5

Explanation of graphs for least squares, link ratio, and budgeted loss methods (3)

Answer 5

least squares - line w/intercept
link ratio - straight line through origin
budget loss - horizontal line

Question 6

Advantages of the Least Squares method over a pure Bayesian estimate (3)

Answer 6

1. simpler to compute
2. easier to explain
3. less dependent on underlying distribution

Question 7

Development formula for Least Squares and ratio results

Answer 7

L(x) = (x - E[X]) * [ covariance(X,Y) / var(X) ] + E[Y]

if ratio = 1&raquo_space; BF
if ratio < 1&raquo_space; budgeted loss
if ratio > 1&raquo_space; link ratio

Question 8

Credibility form of Least Squares development formula

Answer 8

L(x) = Z * (x / d) + (1 - Z) * E[Y]

where Z = bd = b / c if using Least Squares
where Z = VHM / (VHM + EVPV) w/large systematic distortions
and x / d = link ratio estimate w/ d = % emerged

Question 9

Variability represented by VHM and EVPV

Answer 9

VHM = variability from loss occurrence process -- blame UW
EVPV = variability from loss reporting process -- blame claims

Question 10

VHM formula

Answer 10

VHM = d^2 x sigma(Y)^2

Question 11

EVPV formula

Answer 11

EVPV = sigma(d)^2 x ( sigma(Y)^2 + (EY)^2)

Question 12

When to use the credibility form of the development formula

Answer 12

when systematic distributions are too large to be corrected for

Question 13

Potential reserve adjustments to a higher percent reported (3 + justification)

Answer 13

1. Decrease the reserve by a corresponding amount (BL) - appropriate with speedup in reporting
2. Leave the reserve as a % of expected loss (BF) - appropriate if a random large loss drives higher % reported
3. Increase the reserve by a corresponding amount (CL) - appropriate with low confidence in expected loss estimate

Question 14

Interpretation of Cov(X,Y) / Var(X) ratio in the development formula

Answer 14

If ratio is < 1, means that the ultimate loss increases at a slower pace than the increase in reported losses

Question 15

Caseload effect and formula

Answer 15

d can be dependent on Y and Least Squares still works

if for small y, claims are reported more quickly, therefore d is larger for small y.

similarly if there is a large weather event, y is large and many claims are reported quickly, d will also be large

L(x) = Z * (x - x-not) / d + (1 - Z)*E[Y]

where E[X | Y] = d + x-not / y
and Z = VHM / (VHM + EVPV)