Abstract
In this paper, we present a stochastic model for disability insurance contracts. The model is based on a discrete time non-homogeneous semi-Markov process (DTNHSMP) to which the backward recurrence time process is introduced. This permits a more exhaustive study of disability evolution and a more efficient approach to the duration problem. The use of semi-Markov reward processes facilitates the possibility of deriving equations of the prospective and retrospective mathematical reserves. The model is applied to a sample of contracts drawn at random from a mutual insurance company.
Highlights
Non-homogeneous semi-Markov processes were defined independently by Hoem (1972) and IosifescuManu (1972)
The discrete time nonhomogeneous semi-Markov reward process with initial backward recurrence time is studied in Howard (1971) using recursive equations and more recently new results have been presented by Stenberg et al (2007)
The section presents a short introduction to discrete time non-homogeneous semi-Markov process (DTNHSMP) considering initial and final backward times
Summary
Non-homogeneous semi-Markov processes were defined independently by Hoem (1972) and IosifescuManu (1972). A generalization of the transition probabilities of the discrete time non-homogeneous semi-Markov process (DTNHSMP) can be obtained by introducing the initial and final backward times (see D’Amico et al, 2009; D’Amico et al, 2010). The discrete time nonhomogeneous semi-Markov reward process with initial backward recurrence time is studied in Howard (1971) using recursive equations and more recently new results have been presented by Stenberg et al (2007). In this paper we generalize the results obtained in D’Amico et al (2009) by introducing the reward structure. To the best of our knowledge, this is the first time that the general formulae of a DTNHSMP with rewards and initial and final backward times have been presented together with their corresponding mathematical reserves.
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