Skip to content

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

When setting up Thiele's differential equation for a multiple state policy reserve in state i, which term represents the effect of a lump-sum benefit b_ij paid on transition from i to j?

The term is the transition intensity times the sum of the lump-sum benefit and the difference between the reserve in the new state and the reserve in the current state. This captures both the payment and the change in required reserve.

  1. AIntensity μ_ij(t) multiplied by (b_ij + reserve in state j − reserve in state i)Correct
  2. BIntensity μ_ij(t) multiplied by b_ij only
  3. CForce of interest multiplied by b_ij
  4. DIntensity μ_ij(t) multiplied by (reserve in state i − b_ij)
  5. Sum of all intensities from i multiplied by the reserve in state i

Explanation

Thiele's equation includes, for each possible transition, the intensity times the sum of the transition benefit and the change in reserve (V_j − V_i). Using only b_ij ignores the reserve strain from moving to a new state.

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