Multi-state model simulator
The illness-death model is where CS2's Markov theory earns its keep. Move the four transition intensities and watch the healthy, sick and dead occupancy probabilities evolve, then see what the sickness benefit actually costs.
Occupancy probabilities from Healthy at time 0
Transition intensities (per year)
Sickness benefit pricing
EPV of £1 pa while healthy13.88
EPV of £1 pa while sick2.33
Net premium while healthy£3,352 pa
Constant intensities over a 40-year horizon, so this is the time-homogeneous model: occupancy probabilities solve the Kolmogorov forward equations, integrated numerically here. The premium uses the equivalence principle, with £20k a year paid while sick funded by a level premium paid while healthy, both continuous. Push recovery ρ down and watch the sick curve fatten and the premium climb.
Reading the curves
A Markov jump process is fully described by its transition intensities, and the occupancy probabilities solve the Kolmogorov forward equations. With constant intensities the healthy and sick curves settle towards a balance where flows in and out of the sick state offset, before mortality drags both to zero; dead is absorbing, so its curve only ever rises. The classic exam moves are all here: writing down the generator matrix, solving for the probability of being sick at time t, and pricing a benefit as an integral of discounted occupancy probabilities. Try setting recovery to zero and watch the model collapse to the simpler permanent-disability version.
Make it stick. The discrete-time cousin of this model is the no-claims discount simulator, and mortality-only survival lives in the survival models playground. Memori is a flashcard app built by actuarial students, with a ready-made CS2 set in the shop. Join the beta.
For education only: illustrative constant intensities, not a pricing basis and not financial advice.