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
EVPV = variability from loss reporting process

Question 10

VHM formula

Answer 10

VHM = E[X / Y] ^2 * Var(Y)

Question 11

EVPV formula

Answer 11

EVPV = Var(X / Y) * E[Y^2]

= Var(X / Y) * (Var(Y) + E[Y]^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

Process for iterating Least Squares

Answer 13

start with most mature years (move right to left on triangle) but y always = ultimate

Question 14

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

Answer 14

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 15

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

Answer 15

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

Question 16

Caseload effect form of the development formula

Answer 16

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

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