Skip to content

IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events

In a continuous-time Markov jump model with states H (healthy), S (sick) and D (dead), the transition intensity from H to S at age x is defined as the limit of which quantity as h tends to 0 from above?

The H to S intensity is the limit as h tends to zero of the probability of being in S at age x+h, given H at age x, divided by h. It is an instantaneous rate of transition per unit time.

  1. AP(in S at age x+h | in H at age x) divided by hCorrect
  2. BP(in S at age x+h | in H at age x) multiplied by h
  3. CP(in H throughout [x, x+h] | in H at age x) divided by h
  4. DP(in D at age x+h | in H at age x) divided by h
  5. P(in S at age x | in H at age x+h) divided by h

Explanation

The intensity is the limit of h-step transition probability divided by h, i.e. the derivative of the transition probability at h=0. Dividing, not multiplying, gives a rate. Option 3 relates to the holding probability, and option 4 describes a different transition (H to D).

Did you get it right without looking?

One question tells you little. A timed set on Valuing cashflows contingent on multiple transition events shows your real accuracy, how long you take and where you lose marks.

Practise Valuing cashflows contingent on multiple transition eventsFree diagnostic mock

More Valuing cashflows contingent on multiple transition events questions