Semi-Markov reward models under enlarged filtrations with applications to disability insurance

This paper proposes a discrete-time non-homogeneous Semi-Markov reward model designed to describe the evolution of health states for disability insurance applications. The model incorporates the duration dependence of transitions and allows for the inclusion of anticipative information through an enlarged filtration framework (ELF), which provides insights into the insured's potential future health trajectory. Within this setting, we derive recursive evolution equations for the expected discounted rewards and show how these can be used for the computation of premiums. The theoretical framework is complemented by an empirical application based on gender- and age-specific transition probabilities, highlighting how anticipative information reduces uncertainty in disability transitions and significantly affects actuarial valuations. The proposed model thus contributes to a better understanding of longevity and disability risks in multi-state disability insurance contracts.