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Semi-Markov reward models for disability insurance. (English) Zbl 1141.60056

The authors develop a method for calculating not only expectations of accumulated rewards for semi-Markov disability insurance models but also higher order moments for accumulated rewards for disability insurance contracts. This approach allows to compare contracts not only on the base of expected accumulated rewards, but also to perform a full-scale profit-risk analysis and comparison of insurance contracts based, for example, on various criteria combining expected rewards and variances of rewards for different contracts. The method is illustrated by presenting examples based on the real data. In the model considered in this paper, moments of different order for rewards accumulated up to fixed time depend not only of initial states but also of time variable. The authors pay attention to analysis of statistical evidences, which confirm the relevance of semi-Markov setting for disability insurance applications.

MSC:

60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
60K15 Markov renewal processes, semi-Markov processes
91B30 Risk theory, insurance (MSC2010)
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