Exam FAM – SOA Questions and
Answers
annuity certain - Correct Answers -(1 - v^n )/ d
Structured Settlement top down vs bottom up - Correct Answers -Two approaches can
be used to determine the annuity payments in a structured settlement:
Top-down approach: Determine an appropriate lump sum amount, then convert that
amount to an annuity
Bottom-up approach: Determine an appropriate income stream, then calculate the EPV
of the payments
The bottom-up approach is more suitable for structured settlements as their objective is
to match the pre- injury income of the IP.
coinsurance on homeowners insurance (Formula) - Correct Answers -if coinsurance
requirement isn't met (amount that needs to be covered ) then the benefit is =
L*(amount covered/(coinsurance * value at time of loss))
|f the factor applied to loss is greater than 1 then it's just L
If you have a short "death benefit is policy value" whats a trick you can use - Correct
Answers -if you have premium by equivalence you should know the policy value at
beginning and end so you can use the recursive formula to get two formulas for P
u|t q x means what - Correct Answers -the u year deferred probability a life aged x dies
in time (u,u+t)
expense policy value - Correct Answers -EPV(expenses) - EPV(expense loading)
(where expense loading is G-P or just Pe if you need to find that for the solution)
On Level premium when you have rating factors in addition to trend like age and risk
class - Correct Answers -Base level premium * trend ^ number of years * current rating
factors
what to do with censored data in KM or NA estimators of survival - Correct Answers -
Include them in the risk pool r and then take them out at the value specified (so if it's at
least 50 include it in r but when you get a d>50 it's removed from r and isn't included in
the ds)
, mean excess loss function - Correct Answers -e(d)= E[X-d | X>d] = (E[X] -E[X^d])/(1-
F(d))
What is covered by marine insurance - Correct Answers -The following risks are eligible
for coverage under inland marine insurance:
Domestic shipments made by railroad, motor vehicle, or ship on inland waterways.
Provision is made for insuring goods transported by air, mail, parcel post, express,
armored car, or messenger.
Instrumentalities of transportation and communication, such as bridges, tunnels, piers,
wharves, docks, communication equipment, and movable property.
Personal property floater risks used for coverage of construction equipment, personal
jewelry and furs, agricultural equipment, and animals.
PV of whole life with constant interest and force of mortality - Correct Answers -integral
from 0 to infinity of mu*e^-(mu+delta)
Reserves are added to what when determining ultimate losses and why - Correct
Answers -Reserves are added to paid losses (not incurred) since we are trying to
estimate the ultimate paid amounts. IBNP amounts are included in the reserve so we
would be double counting them.
What makes risk insurable? (how many) - Correct Answers -6
Economically Feasible
Economic Value is calcuable
loss is definite
loss is random
exposures in a rate class are homogenous
exposure units are spatially and temporally independent
Delta of a put - Correct Answers --Phi(-d1)
the better term insurance and annuity formula. REMEMBER ME - Correct Answers -Ax
+ nEx * Ax+n
f(x) in terms of other things - Correct Answers -= tpx * mu x+t
Continuous Ax integral value - Correct Answers -Integral from 0 to t of v^t npx force of
mortality
generally gonna be integral of force of mortality * e^(delta + force of mortality)*t
continuous ax integral value - Correct Answers -integral from 0 to of v^t npx
generally gonna be integral of e^(force + delta)*t
Answers
annuity certain - Correct Answers -(1 - v^n )/ d
Structured Settlement top down vs bottom up - Correct Answers -Two approaches can
be used to determine the annuity payments in a structured settlement:
Top-down approach: Determine an appropriate lump sum amount, then convert that
amount to an annuity
Bottom-up approach: Determine an appropriate income stream, then calculate the EPV
of the payments
The bottom-up approach is more suitable for structured settlements as their objective is
to match the pre- injury income of the IP.
coinsurance on homeowners insurance (Formula) - Correct Answers -if coinsurance
requirement isn't met (amount that needs to be covered ) then the benefit is =
L*(amount covered/(coinsurance * value at time of loss))
|f the factor applied to loss is greater than 1 then it's just L
If you have a short "death benefit is policy value" whats a trick you can use - Correct
Answers -if you have premium by equivalence you should know the policy value at
beginning and end so you can use the recursive formula to get two formulas for P
u|t q x means what - Correct Answers -the u year deferred probability a life aged x dies
in time (u,u+t)
expense policy value - Correct Answers -EPV(expenses) - EPV(expense loading)
(where expense loading is G-P or just Pe if you need to find that for the solution)
On Level premium when you have rating factors in addition to trend like age and risk
class - Correct Answers -Base level premium * trend ^ number of years * current rating
factors
what to do with censored data in KM or NA estimators of survival - Correct Answers -
Include them in the risk pool r and then take them out at the value specified (so if it's at
least 50 include it in r but when you get a d>50 it's removed from r and isn't included in
the ds)
, mean excess loss function - Correct Answers -e(d)= E[X-d | X>d] = (E[X] -E[X^d])/(1-
F(d))
What is covered by marine insurance - Correct Answers -The following risks are eligible
for coverage under inland marine insurance:
Domestic shipments made by railroad, motor vehicle, or ship on inland waterways.
Provision is made for insuring goods transported by air, mail, parcel post, express,
armored car, or messenger.
Instrumentalities of transportation and communication, such as bridges, tunnels, piers,
wharves, docks, communication equipment, and movable property.
Personal property floater risks used for coverage of construction equipment, personal
jewelry and furs, agricultural equipment, and animals.
PV of whole life with constant interest and force of mortality - Correct Answers -integral
from 0 to infinity of mu*e^-(mu+delta)
Reserves are added to what when determining ultimate losses and why - Correct
Answers -Reserves are added to paid losses (not incurred) since we are trying to
estimate the ultimate paid amounts. IBNP amounts are included in the reserve so we
would be double counting them.
What makes risk insurable? (how many) - Correct Answers -6
Economically Feasible
Economic Value is calcuable
loss is definite
loss is random
exposures in a rate class are homogenous
exposure units are spatially and temporally independent
Delta of a put - Correct Answers --Phi(-d1)
the better term insurance and annuity formula. REMEMBER ME - Correct Answers -Ax
+ nEx * Ax+n
f(x) in terms of other things - Correct Answers -= tpx * mu x+t
Continuous Ax integral value - Correct Answers -Integral from 0 to t of v^t npx force of
mortality
generally gonna be integral of force of mortality * e^(delta + force of mortality)*t
continuous ax integral value - Correct Answers -integral from 0 to of v^t npx
generally gonna be integral of e^(force + delta)*t
