On probability distributions of present values in life insurance
type: Item
instance of: scholarly article
title: On probability distributions of present values in life insurance
zbMATH Open document ID: 0855.62096
DOI: 10.1016/0167-6687(95)00026-7
author: Ole Hesselager
author: Ragnar Norberg
published in: Insurance Mathematics \& Economics
publication date: 1997-02-09T00:00:00Z
review text: Section 2 deals briefly with models involving only a finite number of random variables. In such situations the distributions of present values (and any other functions of the random variables) can be obtained by integrating the finite-dimensional distribution. This approach comes down overagainst more complex situations where stochastic processes have to be employed. In Section 3 we consider a general multistate insurance policy with payments of assurance and annuity types and with state-dependent force of interest. Assuming that the state process is Markov, we derive in Section 4 a set of integral equations for the conditional probability distribution function of the present value of future benefits less premiums, given the state at the time of consideration. The equations are converted to a differential form that constitutes the basis of a computational scheme. Examples of applications, including numerical illustrations, are given in Section 5.
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 923766
zbMATH Keywords: multistate life insurance
zbMATH Keywords: Markov counting process
zbMATH Keywords: state-dependent force of interest
zbMATH Keywords: integral equations
zbMATH Keywords: conditional probability
zbMATH Keywords: numerical illustrations
MaRDI profile type: Publication
full work available at URL: 0167-6687(95)00026-7
OpenAlex ID: W2075212148
cites work: Differential equations for moments of present values in life insurance
cites work: A time‐continuous markov chain interest model with applications to insurance
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description: scientific article; zbMATH DE number 923766