Tx is the future lifetime of a person aged x.
T is shortening of T0
ω is the Limiting age of a person (max age person can reach – usually 100 – 120 in models)
Define Fx(t) - tqx
Fx(t) is the distribution function of Tx
In actuarial notation, Fx(t) is tqx
Fx(t) = P[Tx ≤ t]
This represents the probability of death for a life aged x by age x + t.
Example. The probability of a 40 year-old dying in the next 20 years is denoted by F40(20) = P[T40 ≤ 20].
Define Sx(t) - tpx
Sx(t) is the survival function of Tx
In actuarial notation Sx(t) is tpx
Sx(t), represents the probability that a life, aged x, survives for t years:
Sx(t) = P[Tx > t]
Example. The probability of a 40 year-old surviving for the next 20 years is denoted by S40(20) = P[T40 > 20].
μx is the force of mortality at age x