Venter Flashcards

1
Q

Incremental age-to-age factor

Venter

A

f(d) = incremental loss / prior cumulative loss

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2
Q

Tests of loss emergence (2)

Venter

A
  1. significance of factors
  2. superiority of alternative emergence patterns
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3
Q

Test for significance of factors (and adjustment if measuring cumulative LDFs)
(Venter)

A

to be significant, a factor should be >= 2x it’s standard deviation

*if age-to-age factors are cumulative, test whether (factor -1) is significant

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4
Q

Tests for superiority of alternate emergence patterns, implication of alternate emergence pattern, and definition of n and p (3)
(Venter)

A
  1. adjusted SSE
  2. AIC
  3. BIC

*implies that the linearity assumption fails

n = # predicted points (= # cells less 1st column)
p = # parameters
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5
Q

Adjusted SSE formula

A

adjusted SSE = SSE / (n - p)^2

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6
Q

AIC formula

Venter

A

AIC = SSE * exp(2p / n)

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7
Q

BIC formula

Venter

A

BIC = SSE * n^(p / n)

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8
Q

Alternative emergence patterns (2)

A
  1. linear w/constant - E[q(w,d+1)|d)] = f(d)*c(w,d) + g(d)
    f is incremental LDF, c is cumulative losses at age d
    g(d) = average incremental loss at age d
    => LS type method
  2. factor * parameter - E[q(w,d) | d] = f(d)*h(w)
    think of f as % emerged in period d
    think of h as estimate of ult loss for AY w
    => BF type method
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9
Q

Loss emergence from linearity assumption

A

expected incremental loss in next period given data to date = f(d) * cum loss to date

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10
Q

Number of parameters in the CL, BF, and CC methods

Venter

A
CL = #AYs - 1
BF = 2 * (#AYs - 1)
CC = same as CL
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11
Q

f(d) in CL vs. BF/CC methods

Venter

A

CL: f(d)’s are link ratios

BF/CC: f(d)’s are lag factors (incremental % reported)

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12
Q

Explain how the CC method is a reduced parameter version of the BF method

A

special case that uses h(w) = h (constant AY parameter across AYs)

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13
Q

Ways to reduce the number of parameters (4)

A
  1. assume the same AY level across several years
  2. assume subsequent development periods have the same % development
  3. fit a trend line through BF ultimate loss parameters
  4. group AYs with similar levels and fit an h parameters to each group
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14
Q
Residual tests (2)
(Venter)
A
  1. linearity of development factors
  2. stability of development factors
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15
Q

Tests of independence (2)

Venter

A
  1. correlation of development factors *»linearity test in Mack
  2. significantly high or low diagonals (CY effects)
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16
Q

Lags (% emerged)

A

lag = incremental age-to-age factor / cumulative age-to-ultimate

= incremental % emergence

17
Q

Fitted h(w) parameters for fitting a parameterized BF model

A

h(w) = sum across row (incremental claims * lag) / sum across row (lag^2)

18
Q

Fitted f(d) parameters for fitting a parameterized BF model

A

f(d) = sum down col (incremental claims * h(w)) / sum down col (h(w)^2)

19
Q

Weighted least squared iterated parameterized BF model and when to use it

A

*use w/o constant variance of residuals

h(w)^2 = sum across row [(incremental claims^2) / lag] / sum across row (lag)

f(d)^2 = sum down col [(incremental claims^2) / h(w)] / sum down col (h(w))

20
Q

Adjustment to h(w) parameter when fitting a parameterized CC

A

single h value summed across all AYs

21
Q

Residual test for linearity

Venter

A

plot raw residuals against previous cumulative losses for a given age

> > strings of positive and negative residuals in a row indicate a non-linear process

22
Q

Types of tests for stability of development factors (3)

Venter

A
  1. residuals against time (AY) - strings of positive and negative residuals in a row indicate instability
  2. plot a moving average of a specific age-to-age factor - shifts in level over time indicates instability
  3. state-space model - compares degree of instability around mean to instability in mean itself over time
23
Q

Adjustments to make if development factors are unstable (2)

A
  1. select a weighted average giving more weight to more recent years
  2. adjust triangle (ex: Berquist Sherman)
24
Q

Venter’s test for correlation of development factors

A

r = CORREL(y,x)

T = r * [ (n - 2) / (1 - r^2) ]^.5
n = # items compared

Reject H0 if absolute value (T) > t-statistic with n-2 df

25
Q

Interpretation of significance level in Venter’s test for correlation of development factors (= AY independence)

A

acceptable % of column pairs that could be correlated by random chance

26
Q

Test for significantly high or low diagonals (CY effects)

Venter

A

create a regression matrix

  • first column = incremental losses starting w/2nd column
  • subsequent columns (one for each age) = previous cumulative losses that inform the incremental losses in column #1
  • dummy columns = 1s or 0s to indicate if the loss is on diagonal (skip first diagonal)

> > if dummy column coefficients are significant, assume there are significant CY effects

27
Q

Threshold for acceptable number of correlated column pairs (Venter)

A

Threshold = 0.1m + sqrt(m)

Where m = # of column pairs tested.