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

A health-sickness-death model has constant intensities: H to S 0.10, H to D 0.02, S to H 0.30, S to D 0.06. Which is the correct Kolmogorov forward equation for d/dt of t p_HH?

The equation is d/dt p_HH = -0.12 p_HH + 0.30 p_HS, because total exit intensity from H is 0.12 and the only inflow into H comes from S at intensity 0.30.

  1. A-0.12 p_HH + 0.30 p_HSCorrect
  2. B-0.12 p_HH + 0.10 p_HS
  3. C-0.36 p_HH + 0.10 p_HS
  4. D-0.10 p_HH + 0.30 p_HS
  5. -0.12 p_HH + 0.36 p_HS

Explanation

The forward equation is the inflow from other states times their intensities into H, minus the outflow from H times p_HH. Outflow from H is 0.10+0.02=0.12. Inflow is from S to H at 0.30 times p_HS. Hence -0.12 p_HH + 0.30 p_HS.

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