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Hattendorff’s theorem and Thiele’s differential equation generalized
Dissertation (MSc (Actuarial Science))--University of Pretoria, 2007.
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| Format: | Thesis |
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University of Pretoria
2013
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| _version_ | 1867613625036832768 |
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| access_status_str | Open Access |
| author2 | Swart, Johan |
| author_browse | Swart, Johan |
| author_facet | Swart, Johan |
| collection | Thesis |
| dc_rights_str_mv | © 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. |
| description | Dissertation (MSc (Actuarial Science))--University of Pretoria, 2007. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/30476 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:39:06.697Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/30476 Hattendorff’s theorem and Thiele’s differential equation generalized Swart, Johan upetd@ais.up.ac.za Messerschmidt, Reinhardt Stochastic processes Point processes Lebesgue-stieltjes integration Discounting Hattendorff’s theorem Thiele’s differential equation UCTD Dissertation (MSc (Actuarial Science))--University of Pretoria, 2007. 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. Insurance and Actuarial Science unrestricted 2013-09-07T19:10:03Z 2006-02-20 2013-09-07T19:10:03Z 2005-02-17 2007-02-20 2006-02-20 Dissertation 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 > http://hdl.handle.net/2263/30476 http://upetd.up.ac.za/thesis/available/etd-02202006-153247/ © 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. application/pdf University of Pretoria |
| spellingShingle | Stochastic processes Point processes Lebesgue-stieltjes integration Discounting Hattendorff’s theorem Thiele’s differential equation UCTD Hattendorff’s theorem and Thiele’s differential equation generalized |
| title | Hattendorff’s theorem and Thiele’s differential equation generalized |
| title_full | Hattendorff’s theorem and Thiele’s differential equation generalized |
| title_fullStr | Hattendorff’s theorem and Thiele’s differential equation generalized |
| title_full_unstemmed | Hattendorff’s theorem and Thiele’s differential equation generalized |
| title_short | Hattendorff’s theorem and Thiele’s differential equation generalized |
| title_sort | hattendorff s theorem and thiele s differential equation generalized |
| topic | Stochastic processes Point processes Lebesgue-stieltjes integration Discounting Hattendorff’s theorem Thiele’s differential equation UCTD |
| url | http://hdl.handle.net/2263/30476 http://upetd.up.ac.za/thesis/available/etd-02202006-153247/ |