Actuary Certification Actuary Certification Life Contingencies 1 — Questions and Answers
Question 1: What does the curtate future lifetime K(x) represent for a life aged x?
- The complete future lifetime in continuous time
- The integer part of the future lifetime (Correct answer)
- The expected remaining years at exact age x
- The force of mortality at age x
Correct answer: The integer part of the future lifetime
K(x) is the curtate future lifetime, defined as the greatest integer less than or equal to the complete future lifetime T(x).
Question 2: The probability that a life aged 30 survives to age 40 is denoted as:
- q30
- 10p30 (Correct answer)
- 10q30
- p40
Correct answer: 10p30
The notation nPx represents the probability that a life aged x survives at least n more years, so 10p30 is the probability of surviving from 30 to 40.
Question 3: Which life table function gives the expected number of deaths between exact ages x and x+1 out of a cohort of l0 lives?
- lx
- dx (Correct answer)
- qx
- mx
Correct answer: dx
dx = lx − lx+1 represents the number of deaths between ages x and x+1 in the life table cohort.
Question 4: The force of mortality μ(x) is best described as:
- The probability of death in the next year
- The instantaneous rate of mortality at exact age x (Correct answer)
- The expected lifetime from birth
- The number of survivors at age x
Correct answer: The instantaneous rate of mortality at exact age x
The force of mortality μ(x) is the instantaneous hazard rate of death, analogous to an intensity in a Poisson process.
Question 5: Under the Uniform Distribution of Deaths (UDD) assumption, qx+t for 0 < t < 1 equals:
- t · qx (Correct answer)
- (1−t) · qx
- qx / t
- qx^t
Correct answer: t · qx
Under UDD, deaths are uniformly distributed within each year of age, so the probability of death in the first t years of age x is t·qx.
Question 6: The net single premium for a whole life insurance of 1 payable at the moment of death for (x) is denoted:
- Ax
- äx
- ax
- Āx (Correct answer)
Correct answer: Āx
Āx (A-bar-x) is the APV of a whole life insurance of 1 payable at the moment of death, using continuous discounting.
Actuary Certification Actuary Certification Life Contingencies 1
What does the curtate future lifetime K(x) represent for a life aged x?