Exam FAM – SOA UPDATED ACTUAL
Exam Questions and CORRECT Answers
annuity certain - CORRECT ANSWER - (1 - v^n )/ d
Structured Settlement top down vs bottom up - CORRECT ANSWER - 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 ANSWER - 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
ANSWER - 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 ANSWER - the u year deferred probability a life aged x
dies in time (u,u+t)
expense policy value - CORRECT ANSWER - 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 ANSWER - Base level premium * trend ^ number of years * current rating
factors
what to do with censored data in KM or NA estimators of survival - CORRECT
ANSWER - 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 ANSWER - e(d)= E[X-d | X>d] = (E[X] -
E[X^d])/(1-F(d))
What is covered by marine insurance - CORRECT ANSWER - 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 ANSWER -
integral from 0 to infinity of mu*e^-(mu+delta)
Reserves are added to what when determining ultimate losses and why - CORRECT
ANSWER - 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 ANSWER -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 ANSWER - -Phi(-d1)
the better term insurance and annuity formula. REMEMBER ME - CORRECT
ANSWER - Ax + nEx * Ax+n
f(x) in terms of other things - CORRECT ANSWER - = tpx * mu x+t
Continuous Ax integral value - CORRECT ANSWER - 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 ANSWER - integral from 0 to of v^t npx
generally gonna be integral of e^(force + delta)*t
tqx in terms of fx Fx Sx - CORRECT ANSWER - tqx = Fx(t)
Tips for finding value of an insurance/annuity in terms of other annuities - CORRECT
ANSWER - Stay organized,
keep writing down relationships until something clicks.
Exam Questions and CORRECT Answers
annuity certain - CORRECT ANSWER - (1 - v^n )/ d
Structured Settlement top down vs bottom up - CORRECT ANSWER - 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 ANSWER - 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
ANSWER - 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 ANSWER - the u year deferred probability a life aged x
dies in time (u,u+t)
expense policy value - CORRECT ANSWER - 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 ANSWER - Base level premium * trend ^ number of years * current rating
factors
what to do with censored data in KM or NA estimators of survival - CORRECT
ANSWER - 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 ANSWER - e(d)= E[X-d | X>d] = (E[X] -
E[X^d])/(1-F(d))
What is covered by marine insurance - CORRECT ANSWER - 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 ANSWER -
integral from 0 to infinity of mu*e^-(mu+delta)
Reserves are added to what when determining ultimate losses and why - CORRECT
ANSWER - 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 ANSWER -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 ANSWER - -Phi(-d1)
the better term insurance and annuity formula. REMEMBER ME - CORRECT
ANSWER - Ax + nEx * Ax+n
f(x) in terms of other things - CORRECT ANSWER - = tpx * mu x+t
Continuous Ax integral value - CORRECT ANSWER - 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 ANSWER - integral from 0 to of v^t npx
generally gonna be integral of e^(force + delta)*t
tqx in terms of fx Fx Sx - CORRECT ANSWER - tqx = Fx(t)
Tips for finding value of an insurance/annuity in terms of other annuities - CORRECT
ANSWER - Stay organized,
keep writing down relationships until something clicks.
