CAS Exam 7 UPDATED Actual Exam Questions and CORRECT Answers
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CAS
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CAS
CAS Exam 7 UPDATED Actual Exam
Questions and CORRECT Answers
If Claim Counts are Poisson(m), and
d = probability of reporting in first period
What is the Bayes Reserve? - CORRECT ANSWER- R(x) = mu(1 - d)
List the 3 Special Cases for Brosius Least Squares - CORRECT ANSWER- y = a + bx |
Least...
CAS Exam 7 UPDATED Actual Exam
Questions and CORRECT Answers
If Claim Counts are Poisson(m), and
d = probability of reporting in first period
What is the Bayes Reserve? - CORRECT ANSWER- ✔✔R(x) = mu(1 - d)
List the 3 Special Cases for Brosius Least Squares - CORRECT ANSWER- ✔✔y = a + bx |
Least Squares | Restriction
y = bx | Chainladder | a=0
y = a + x | Bornhuetter-Ferguson | b=1
y = a | Budgeted Loss | b=0
Claim Counts are NegBin(r, p)
d is the probability of reporting in the first period
x is the actual reported in the first period
What is the Bayes Reserve? - CORRECT ANSWER- ✔✔R(x) = [s /(1 - s)](x + r)
s = (1 - d)(1 - p)
Negative Binomial Distribution - CORRECT ANSWER- ✔✔Y ~ NegativeBinomial(r, p)
E[Y] = r(1 - p)/p
For Ultimate Losses Y, and Reported Losses X What is the Best Linear estimate of Y given
x? - CORRECT ANSWER- ✔✔L(x) = [x - EX][Cov(X,Y)/Var(X)] + EY
What are the formulas for a and b in Brosius Least Squares? - CORRECT ANSWER- ✔✔b =
(E(xy) - E(x)E(y)) / (E(x^2) - E(x)^2)
a = E(y) - bE(x)
,Estimate Ultimate Losses L(x) using a credibility formula? - CORRECT ANSWER- ✔✔L(x)
= Zx/d + (1 - Z)EY
Z = VHM/(VHM + EVPV)
VHM = VarY[E(X | Y)]
EVPV = EY[Var(X | Y)]
When is Brosius Least Squares Appropriate? Inappropriate? - CORRECT ANSWER- ✔✔-
Appropriate: When the Distribution is the same across multiple years
- Inappropriate: Year to Year changes are due to systemic shifts, eg. inflation, legal
environment
Calculate the Statistics used in Brosius - CORRECT ANSWER- ✔✔b = (E(xy) - E(x)E(y)) /
(E(x^2) - E(x)^2)
a = E(y) - bE(x)
LDF: c = E(y)/E(x)
Credibility: Z = b / c
%Reported: d = 1 / c
Estimate Ultimate Losses L(x) using a credibility formula when given mean and variance of
Ultimate losses and the development pattern - CORRECT ANSWER- ✔✔L(x) = Zx/d + (1 -
Z)EY
Z = VHM/(VHM + EVPV)
,VHM = (d^2) (sigmay^2)
EVPV = (sigmad^2)[(sigmay^2) + (EY)^2]
d = expected % paid to date
Definition of an exposure and an exposure base - CORRECT ANSWER- ✔✔An exposure is
the basic unit of risk underlying the insurance premium.
The definition of what an exposure represents varies by line of business and sometimes
coverage and is called an exposure base.
Short Formula for the Benktander Reserve - CORRECT ANSWER- ✔✔RGB = (qk)x(UBF)
qk = % Unreported at Age k
UBF = Ultimate losses from Bornhuetter-Ferguson Method
Hurlimann - Calculate the Collective Loss Ratio Reserve Estimate - CORRECT ANSWER-
✔✔RColl = q (V * ELR)
V = Premium (or other exposure base, used to calculate ELR)
This is similar to the BF method
Hurlimann - Calculate the Individual Loss Ratio Reserve Estimate - CORRECT ANSWER-
✔✔Rind = C/p - C
p = % Reported
C = Paid to Date
This is similar to the CL method
Calculate % Reported, according to Hurlimann - CORRECT ANSWER- ✔✔mk = sum(
Losses in Column k) / sum(Corresponding Premium)
ELR = Sum(mk)
pk = Percent Paid to Date by age k
pk = (1/ELR) * sum from j to k of (mj)
Hurlimann - Full Credibility Formula - CORRECT ANSWER- ✔✔Z*i = (pi/qi) [(Cov(Ci,Ri)
+ piqiVar(UiBC)]/[Var(Ci) + (pi^2)Var(UiBC)]
UiBC = a priori Ultimate for each AY
6 Components of a Reinsurance Loss Reserve - CORRECT ANSWER- ✔✔1. Case Reserves
(by ceding company)
2. Additional Case Reserves (set by reinsurer)
3. Development on Known Claims (IBNER)
4. Pure IBNR
5. Discount for future investment income(where permitted)
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