# Hattendorff’s theorem and Thiele’s differential equation generalized

 dc.contributor.advisor Swart, Johan en dc.contributor.postgraduate Messerschmidt, Reinhardt en dc.date.accessioned 2013-09-07T19:10:03Z dc.date.available 2006-02-20 en dc.date.available 2013-09-07T19:10:03Z dc.date.created 2005-02-17 en dc.date.issued 2007-02-20 en dc.date.submitted 2006-02-20 en dc.description Dissertation (MSc (Actuarial Science))--University of Pretoria, 2007. en dc.description.abstract Hattendorff's theorem on the zero means and uncorrelatedness of losses in disjoint time periods on a life insurance policy is derived for payment streams, discount functions and time periods that are all stochastic. Thiele's differential equation, describing the development of life insurance policy reserves over the contract period, is derived for stochastic payment streams generated by point processes with intensities. The development follows that by Norberg. In pursuit of these aims, the basic properties of Lebesgue-Stieltjes integration are spelled out in detail. An axiomatic approach to the discounting of payment streams is presented, and a characterization in terms of the integral of a discount function is derived, again following the development by Norberg. The required concepts and tools from the theory of continuous time stochastic processes, in particular point processes, are surveyed. en dc.description.availability unrestricted en dc.description.department Insurance and Actuarial Science en dc.identifier.citation Messerschmidt, R 2005, Hattendorff’s theorem and Thiele’s differential equation generalized, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/30476 > en dc.identifier.upetdurl http://upetd.up.ac.za/thesis/available/etd-02202006-153247/ en dc.identifier.uri http://hdl.handle.net/2263/30476 dc.language.iso en dc.publisher University of Pretoria en_ZA dc.rights © 2005, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. en dc.subject Stochastic processes en dc.subject Point processes en dc.subject Lebesgue-stieltjes integration en dc.subject Discounting en dc.subject Hattendorff’s theorem en dc.subject Thiele’s differential equation en dc.subject UCTD en_US dc.title Hattendorff’s theorem and Thiele’s differential equation generalized en dc.type Dissertation en
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