A theory of bonus life insurance
The paper deals with a sketch of the traditional approach to bonus theory in the framework of a time-continuous Markov chain model for a multi-state insurance policy. In this setup intensities of transitions \(\mu_{jk}(t)\) and intensity of interest \(\delta(t)\) are non-stochastic for the time being. Further, this model is extended by letting the second order experience basis (mortality, interest, etc.) be stochastic. More precise, the author extends the second order model by placing a probabilistic distribution on \(\mu_{jk}(t)\) and \(\delta(t)\) and taking the traditional model as a conditional one given these elements. Special attention is given to a candidate model in which the second order basis is governed by a time-continuous Markov chain \(y(t)\), where \(\delta(t)\) and \(\mu_{jk}(t)\) depend on the current \(y\)-state. A novel definition of the technical surplus of an insurance contract is proposed and main principles for its repayment as bonus are presented. Possibilities of model-based prognoses of future bonuses within such an approach are discussed. Numerical examples are provided.
scientific article; zbMATH DE number 1452406