A theory of bonus life insurance
type: Item
instance of: scholarly article
title: A theory of bonus life insurance
zbMATH Open document ID: 0939.62108
author: Ragnar Norberg
published in: Finance and Stochastics
publication date: 2000-05-24T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 1452406
zbMATH Keywords: bonus theory
zbMATH Keywords: Markov chains
zbMATH Keywords: transition intensities
zbMATH Keywords: stochastic interest
zbMATH Keywords: reserves
zbMATH Keywords: mortality
zbMATH Keywords: conditional model
zbMATH Keywords: technical surplus
MaRDI profile type: Publication
full work available at URL: s007800050067
OpenAlex ID: W2031321758
DOI: 10.1007/S007800050067
description: scientific article; zbMATH DE number 1452406