Actuarial Notation

Question 1

Define T_x

Answer 1

• T_x* is the future lifetime of a person aged x.
• T* is shortening of T₀

Question 2

Define ω

Answer 2

ω is the** Limiting age of a person** (max age person can reach – usually 100 – 120 in models)

Question 3

Define F_x(t) - _tq_x

Answer 3

F_x(t) is the distribution function of T_x

In actuarial notation, F_x(t) is _tq_x

F_x(t) = P[T_x ≤ 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].

Question 4

Define S_x(t) - _tp_x

Answer 4

S_x(t) is the survival function of T_x

In actuarial notation S_x(t) is _tp_x

• S_x(t)*, represents the probability that a life, aged x, survives for t years:
• S_x(t) = P[T_x > t]*

Example. The probability of a 40 year-old surviving for the next 20 years is denoted by S₄₀(20) = P[T₄₀ > 20].

Question 5

Define μ_x

Answer 5

μ_x is the force of mortality at age x