Valuation and risk assessment of disability insurance using a discrete time trivariate Markov renewal reward process

In disability insurance, the impact of the duration since the inception of disability on future recovery and mortality rates has been modeled by bivariate Markov renewal processes and the associated semi-Markov process, but these processes do not incorporate potential dependences between the durations in two successive states. Thus, the aim of this paper is to introduce a discrete time trivariate Markov renewal reward model, an associated formula for higher moments and a corresponding simulation that include the potential dependence between the durations, i.e. the inter-arrival times, in two successive states. The proposed model is compared with two alternative models that do not include this dependence.