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. / Dissertation (MSc (Actuarial Science))--University of Pretoria, 2007. / Insurance and Actuarial Science / unrestricted
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:up/oai:repository.up.ac.za:2263/30476 |
| Date | 20 February 2006 |
| Creators | Messerschmidt, Reinhardt |
| Contributors | Swart, Johan, upetd@ais.up.ac.za |
| Publisher | University of Pretoria |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Dissertation |
| 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. |
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