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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Transition intensities dependent on age (exact or census)

In the two-state (alive-dead) model of mortality, which of the following correctly defines the force of mortality at age x?

The force of mortality at age x is the limit, as h approaches zero, of the probability that a life aged x dies within h years divided by h. It is an instantaneous death rate, not the one-year probability q_x.

  1. AThe limit as h tends to 0 of the probability that a life aged x dies within h years, divided by hCorrect
  2. BThe probability that a life aged x dies within one year
  3. CThe ratio of deaths at age x to the initial population at birth
  4. DThe cumulative hazard accumulated from birth to age x
  5. The expected number of years lived by a life aged x

Explanation

The force of mortality is the instantaneous rate of death: mu_x = lim h->0 of (h q_x)/h. The probability of dying within one year is q_x, which is a different quantity. The cumulative hazard is the integral of mu, not mu itself.

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