The Kernel Equations for a Modified Disability Income Insurance Model


  • Sylviani Chandra Universitas Pelita Harapan
  • Helena Margaretha Universitas Pelita Harapan
  • Giovani Gracianti Universitas Pelita Harapan



disability income insurance, semi-Markov model, transition intensities


A disabled worker does not earn enough for a living. Disability income insurance is a long-term guarantee that provides supplementary income when a worker is disabled or dies. In the standard model for disability income insurance, people who recovered from a disability condition are assumed to return to the initial healthy condition (i.e., before being disabled). This assumption might not be realistic. In this paper, we present a modification of the standard disability income insurance model, in which the recovery state is separated from the initial healthy/active state. Disability benefit is given in terms of annuities while the policyholder is disabled. The annuities cease as he/she recovers and resume if he/she becomes disabled again. The death benefit is given if the policyholder dies. To make the model more realistic, we apply semi-Markov assumptions. In this assumption, the length of staying in a condition affects the probability of leaving that condition. We present the kernel equations for the model and take a case study using the US Social Security Administration data for workers born in 1996 with an age range of 20 to 62 years. We calculate the transition probabilities and premiums for some examples of insurance products.



2022-04-24 — Updated on 2022-04-24