Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

I LIKE WOMEN > Final Review > Flashcards

Final Review Flashcards

1
Q

Benktander

Formula and Pro/Cons

A

% reported * C-L Ult + % unreported * B-F Ult

Cum Losses + % unreported * B-F Ult

Advantages:
* Almost always has a smaller MSE than C-L and B-F Method
* Incorporates prior expectation of losses rather than fulyl relying on paid/reported losses to date (like the C-L)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Hurlimann

Ult, Credibility, ELR, p

A

Ult = Z * C-L Ult + (1-Z) B-F Ult

Credibility Z
* Z(GB) = p = % reported
* Z(WN) = p * ELR
* Z(OC) = p / [ p+sqrt(p) ] = p / ( p + t )

ELR
* m = incremental LR = sum(loss) / sum(premium)
* ELR = sum(m’s)

p = sum(m’s) / ELR for each AY

C-L = Individual | B-F = collective

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Hurlimann

What Happens When Var(U) > Var(U_bc)?

A
  • f increases
  • t increases
  • Z decreases
  • more weight to B-F (collective) method
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Brosius

What Happens When Intercept or Slope < 0?

A

Set intercept = 0 (C-L method)

Set slope = 0 (ELR method)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Brosius

Caseload Effect, Credibility Weighted Ultimate

All steps, another way to say VHM/EPV

A

% reported at 12 months = dy + x0
Z = VHM / (VHM + EPV)
VHM = Variation due to Loss Occurrence Process
EPV = Variation due to Loss Reporting Process

L(X) ult = Z * (x - x0)/d + (1-Z) * ELR Ult
USE ORIGINAL SCENARIO FOR ELR ULT

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Brosius

Hugh White’s Question

3 Scenarios

A

Cov(X,Y) = Var(X) –> IBNR unchanged (B-F Method)
Cov(X,Y) < Var(X) –> decrease IBNR (ELR Method)
Cov(X,Y) > Var(X) –> increase IBNR (C-L Method)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Clark

Cape Cod Setup

Weibull

A

X = 6, 18, 30, etc
% Paid = G(X) = 1- exp( -(x/θ)^w )
Used-Up Prem = G(X) * OLEP
% Unpaid = 1 - G(X)
ELR = sum(Cum Loss) / sum(Used-Up Prem)
Ult = Cum Loss + % unreported * ELR * OLEP

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Clark

Log-Likelihood

All steps/formulas

A

Expected Incremental Triangle = Incremental G(X) * ELR Ult

MLE Triangle = Actual * ln(Expected) - Expected
Log-Likelihood = sum(MLE Triangle)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Mack

Reserve Confidence Interval

All Formulas

A

Var = ln(1+ SE(reserves)^2 / reserves^2)
Confidence Interval = Reserves * exp(-Var/2 ± Z * SD)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Venter

Parameterized BF Method: h(w) / f(w)

What is it? + both formula

Variance is assumed to be constant

A

h(w) ~ kind of like ultimate loss, but ONLY to be used with f(d) to get expected reserves
f(d) ~ incremental % reported

If variance assumed to be constant:
* h(w) = sumprod[ f(d), incremental loss ROWS] / sumSQ[ f(d) ]
* f(d) = sumprod[ h(w), incremental loss COLUMNS] / sumSQ[ h(w) ]

w for the years, d for development period

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Venter

Starting f(d) - seed

A

If not given in the problem:
* Incremental % Reported (first get % reported = 1/CDF)
* = incremental LDF / CDF

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Venter

SSE and Adjusted SSE

A

SSE Triangle = (Actual - Expected)^2
SSE = sum(SSE Triangle EXCLUDING 1ST COLUMN)
Adjusted SSE = SSE / (n-p)^2
where n = # of values in triangle excluding the first column
p = number of parameters

C-L and CC: p = d - 1
BF: p = 2d - 2
where d = # of development periods

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Venter

AIC / BIC

A

AIC = SSE * exp(2p/n)
BIC = SSE * n^(p/n)
where n = # of values in triangle excluding the first column
p = number of parameters

C-L and CC: p = d - 1
BF: p = 2d - 2
where d = # of development periods

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Venter

Alternative Emergence Patterns

A

Linear with constant = f(d) * c(w,d) + g(d)
* Highly variable and slowly reporting lines (XS reinsurance)

Factor * Parameter = f(d) * h(w)
* Parameterized BF model
* Cape Cod has h(w) = h (constant)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Shapland

Unscaled Pearson Residual

A

= (actual - expected) / sqrt(expected^z)
USING INCREMENTAL LOSSES

The power, z, is used to specify the error distribution
* z = 0 for normal
* z = 1 for poisson
* z = 2 for gamma
* z = 3 for inverse gaussian

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

Shapland

Standardized Pearson Residual

What is this used for?

A

Unscaled Pearson Residual * hat matrix adj factor
where adj factor = sqrt (1 / (1 - hat matrix value) )

USED TO GET SAMPLED RESIDUALS (r) –> SAMPLED INCREMENTAL LOSS
= r * sqrt(fitted incremental loss) + fitted incremental loss

17
Q

Shapland

Location Mapping

What is it + Pros/Cons

A

There exists correlation between LOBs.

  1. We would sample the residuals for the first LOB
  2. Make a note of that location of that sample
  3. Then sample the other LOBs from the same location

The residuals will be different from the LOBs (separate model, different parameters), but the sampled residual will come from the same location, which helps keep correlation consistent

Pro - Simple to implement in Excel and no need for correlation matrix
Con - Requires all LOBs to use data triangles of the same size with no missing values or outliers

18
Q

Taylor

ODP Cross-Classified GLM Expected Incremental Losses

Setup + Calculation

A

Normalize α’s and β’s so that sum(β’s) = 1
α’s = Expected Ultimate Loss (column)
β’s = Expected Incremental % Reported (row)

Expected Incremental Loss = α’s * β’s

19
Q

Meyers

K-S Test

A

K-S Test
1. Sort Actuals
2. Expected = 100 * (1/n, 2/n, etc)
3. abs difference
4. CV = 136/sqrt(n)
5. if max(abs diff) > CV, then model is invalidated

P-P Plot (SHEAVY TAIL WRONG)
* Graph expected (x-axis) vs actual (y-axis)
* S-shape = light tail (variance too low)
* Reverse S-shape = heavy tail (variance too high)
* U-shape = bias high (mean too high)
* Reverse U-shape = bias low (mean too low)

20
Q

Verrall

Baysian BF Model Incremental Paid

What does higher β imply?

A

Incr Paid = Z * C-L incr paid + (1-Z) * B-F incr paid
Z = p / (βΦ + p)
C-L incr paid = (LDF - 1) * Cum Loss
B-F Incr paid = (Incr % Paid) * ELR Ult
ELR Ult (expert opinion) = M = α / β

Higher β’s means more certain in the expected losses, giving more weight to the B-F method

p = % paid, prior

21
Q

Sahasrabudde

LEV Formula

A

Loss * [ 1-exp(-limit / loss) ]
where loss = claim size model

22
Q

Sahasrabudde

Adjusted Cumulative Losses

A

Cumulative Loss (limited) * LEV(basic limit, last row, same column) / LEV (same limit, same same)

“Bring it to basic limit, latest year”
“But first need to back out current LEV, same same”

ONLY USE THIS TO CALCULATE PRE-ADJUSTED LDFS
DO NOT USE THIS TO CALCULATE IBNR OR ULTS

23
Q

Sahasrabudde

Adjusted LDF (to ult) Formula

What do I apply these LDFs to?

A

Pre-Adjusted LDF (to ult) * numerator / demonimator
num = [ LEV(upper lim, same row, last column) - LEV (lower limit)] / LEV(basic lim last row, last column)
demon = [ LEV(upper lim, same same) - LEV (lower limit)] / LEV(basic lim last row, same column)

Trick - (SLLL) - SAME, LAST LAST LAST
Trick - (SSLS) - SAME, SAME, LAST, SAME

Apply these LDF (to ult) to YTD losses for specific layer

24
Q

Siewert

Implied Development Method

Steps + Pros/Cons

A
  1. Calculate unlimited ult loss using C-L
  2. Calculated limited ult loss using C-L
  3. Excess ult loss = (1) - (2)

Pros
* Incorporates actual loss emergence
* Provides excess loss estimate (at early maturities) even when excess losses have not emerged
* Limited loss LDFs are more stable than excess LDFs

Con - not directly focusing on excess loss development (misplaced focus)

25
Q

Friedland

Which Treaty Best Promotes Stability?

A
  • Non-proportional reinsurance is intended to provide stability by protecting the risks insured by the ceding company’s losses above a limit
  • Proportional reinsurance is intended to provide capacity and surplus relief to ceding
26
Q

Friedland

Loss Portfolio Transfer

A
  • Reinsurer assumes all or part of future loss payments on policies written in prior years
  • AKA - ceding insurer cedes all or part of their reserves (for prior years) to the reinsurer
  • Reinsurer usually takes over claims management
  • Ceding insurer increases surplus (less liabilities)
27
Q

Friedland

Adverse Development Cover

A
  • Ceding company also cedes reserves to reinsurer, but only if they exceed a certain threshold
  • Threshold usually a dollar amount or a multiple of current reserves
  • No transfer of reserves, ceding insurer maintains claims management
28
Q

Friedland

Difficulty Working With Reinsurer’s Loss Triangles

A
  • There is greater volatility in the LDFs factors for reinsurance than with primary insurance
  • Tail factors are often higher for reinsurer’s because losses in higher layers tend to take longer to develop (and because reinsurer has data lag)
29
Q

Friedland

Variability of LDFs on Proportional vs Non-Proportional Reinsurance

A
  • LDFs are more volatile for non-proportional reinsurance than proportional because
  • Non-proportional reinsurance (usually) covers excess losses (above retention) and proportional covers losses from the group up
30
Q

Teng and Perkins

Total Developed Loss n-th Adjustment, L(n)
Capped Loss n-th Adjustment, CL(n)
Expected Premium at n-th Adjustment, P(n)
Expected Incremental Premium at n-th Adjustment, P(n) - P(n-1)

Formula Method

A

L(1) = SP * ELR * %L(1)
CL(1) = L(1) * LCR(1)
P(1) = ( BP + CL(1) * LCF ) * TM
P(2) - P(1) = [ CL(2) - CL(1) ] * LCF * TM

%L(n) = % Losses emerged (cumulative)

31
Q

Teng and Perkins

PDLD Formula Method

Formula Method

A

PDLD(1) = [ BP/SP * TM / (ELR * %L(1) ] + (LCR(1) * LCF * TM)
= (BP + CL(1) * LCF) * TM / L(1)
PDLD(2) = ILCR(2) * LCF * TM

Also:
* PDLD(1) = P(1) / L(1) = (BP + CL(1) * LCF) * TM / L(1)
* PDLD(2) = [ P(2) - P(1) ] / [ L(2) - L(1) ]
* ILCR(2) = [ LCR(2) * %L(2) - LCR(1) * %L(1) ] / [ %L(2) - %L(1) ]
* ILCR(2) = [ CL(2) - CL(1) ] / (L2 - L1)

%L(n) = % Losses emerged (cumulative)

32
Q

Teng and Perkins

PDLD & CPDLD Empirical Method

A

PDLD(1) = Prem(0-27) / Loss(0-18)
PDLD(2) = Prem(28-39) / Loss(19-30)
PDLD(3) = Prem(40-51) / Loss(31-42)
Subsequent = 0

CPDLD(n) = sumproduct(PDLD, % Loss Emerged) / sum(% Loss Emerged)

33
Q

Teng and Perkins

Premium Responsiveness of Teng & Perkin vs Fisk-Gibbon

A

Premium responsiveness decreases over time for Teng & Perkin

Premium responsiveness is constant over time for Fisk-Gibbon

34
Q

Marshall

Risk Margin For Normal and Lognormal Distribution

A

Normal
* Z * CoV
* norminv(%-tile,0,CoV)

Lognormal
* Var = σ^2 = ln(1 + CoV^2)
* Risk margin = exp(-Var/2 + Z * SD) - 1

I LIKE WOMEN (10 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions