Survival Models
This symbol represents the probability that a person aged x will survive at least t more years.
What is t-p-x (or t subscript p subscript x)?
This type of life insurance pays a benefit of 1 immediately upon death.
What is whole life insurance?
This type of annuity makes payments while the annuitant is alive, starting immediately.
What is a life annuity-due?
This principle states that the present value of premiums equals the present value of benefits.
What is the equivalence principle?
This symbol represents the probability that both (x) and (y) survive t years.
What is t-p-xy (or t subscript p subscript xy)?
This function, denoted S(x), gives the probability of surviving from birth to age x.
What is the survival function?
This symbol represents the actuarial present value of a whole life insurance of 1 on (x).
What is Ax (or A subscript x)?
This symbol represents the actuarial present value of a life annuity-due of 1 per year.
What is äx (or a-double-dot subscript x)?
This symbol represents the annual premium for whole life insurance.
What is Px (or P subscript x)?
This type of life insurance pays upon the first death in a group of lives.
What is joint life insurance?
This is the expected number of years a person aged x will live, often denoted as e̊x.
What is the complete expectation of life (or life expectancy)?
This type of insurance pays a benefit only if death occurs within n years.
What is n-year term life insurance?
This type of annuity makes payments for exactly n years, regardless of survival.
What is an n-year certain annuity?
This type of reserve is calculated as the difference between future benefits and future premiums.
What is the benefit reserve (or policy value)?
This status continues as long as at least one person in the group is alive.
What is the last survivor status?
This mortality assumption states that deaths occur uniformly throughout each year of age.
What is the uniform distribution of deaths (UDD)?
This symbol represents the actuarial present value of an n-year endowment insurance.
What is Ax:n̅| (or A subscript x colon n endowment)?
This relationship connects life insurance and annuity present values: Ax + d × äx = ?
What is 1? (This is the fundamental relationship)
This recursive formula relates reserves: tVx = (tVx-1 + Px)(1+i) - qx+t-1
What is the forward recursion formula for reserves?
For independent lives, this equals px × py.
What is pxy (the probability both survive one year)?
This type of mortality law assumes the force of mortality is constant, written as μ(x) = μ.
What is the exponential distribution (or constant force of mortality)?
This type of life insurance has benefits that increase each year, often by (k+1) in year k+1.
What is increasing life insurance?
This type of annuity makes payments for n years if the person survives, and guarantees payments for at least m years.
What is an n-year temporary life annuity with m-year certain guarantee?
This method calculates reserves by considering only future benefits, without subtracting future premiums.
What is the paid-up insurance method?
This type of annuity continues as long as at least one annuitant is alive.
What is a last survivor annuity?