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Continuous affine processes: transformations, Markov chains and life insurance

Published online by Cambridge University Press:  10 June 2016

Kristian Buchardt*
Affiliation:
University of Copenhagen and PFA Pension
*
* Postal address: PFA Pension, Sundkrogsgade 4, DK-2100 Copenhagen O, Denmark. Email address: kristian@buchardt.net

Abstract

Affine processes possess the property that expectations of exponential affine transformations are given by a set of Riccati differential equations, which is the main feature of this popular class of processes. In this paper we generalise these results for expectations of more general transformations. This is of interest in, e.g. doubly stochastic Markov models, in particular in life insurance. When using affine processes for modelling the transition rates and interest rate, the results presented allow for easy calculation of transition probabilities and expected present values.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2016 

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