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On bonus and bonus prognoses in life insurance. (English) Zbl 0979.91045
This paper deals with studying the surplus on a life insurance policy defined as the difference between the second order retrospective reserve and the first order prospective reserve. The author investigates relationships between various notions of surplus and demonstrates how future contributions can be forecasted in an extended model where the empirical basis is driven by a stochastic process. The model is considered as continuous time Markov chain model for the multi-state insurance policy extended with a stochastic environment. The first order basis is taken to be deterministic. The definition of technical surplus is given and the policy’s contribution to this surplus is considered. The author discusses some commonly used schemes for the redistribution of the technical surplus and shows how model-based prognoses of future bonuses can be worked out in the stochastic environment set-up. Numerical illustrations are presented.

MSC:
91B30 Risk theory, insurance (MSC2010)
60J27 Continuous-time Markov processes on discrete state spaces
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