Semi-Markov and Non-Homogeneous Models for LTAM

Semi-Markov Models

In a semi-Markov model, transition intensities depend not only on the current state and age but also on the duration in the current state. This is common in disability insurance, where recovery and mortality rates for disabled lives depend on how long they have been disabled. The transition intensity mu_{x,z}^{ij} depends on age x and duration z in state i. This added complexity makes the model more realistic but requires tracking duration as an additional variable. Calculation of transition probabilities and reserves requires solving systems of integral or differential equations.

Non-Homogeneous Models

Non-homogeneous models allow transition intensities to vary over calendar time, not just age. This captures trends like mortality improvement or changing disability incidence rates. In practice, actuaries often use non-homogeneous models by applying improvement factors to base transition intensities. Exam LTAM tests semi-Markov models primarily in the context of disability insurance, requiring you to set up and solve for reserves and premiums when recovery rates depend on disability duration.