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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Concepts of survival models

In a survival model for a lifetime random variable T_x of a life aged x, the force of mortality at age x+t is defined as the limit of P(T_x ≤ t+h | T_x > t)/h as h tends to 0 from above. Which statement about this quantity is correct?

The force of mortality is the instantaneous rate of death at a given age, conditional on survival to that age. It equals density divided by survival function, is a rate rather than a probability, and can exceed 1 and need not increase.

  1. AIt is the probability density of the age at death at age x+t, unconditional on survival
  2. BIt is the instantaneous rate of death at age x+t, given survival to that age, and is not itself a probabilityCorrect
  3. CIt is the probability of surviving from age x to age x+t
  4. DIt must always be less than or equal to 1
  5. It is always an increasing function of age

Explanation

The force of mortality is f(x+t)/S(x+t), a conditional rate of death per unit time among those alive at x+t. It can exceed 1 and need not increase with age, and it differs from the unconditional density.

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