Title page for ETD etd-02202006-153247


Document Type Master's Dissertation
Author Messerschmidt, Reinhardt
URN etd-02202006-153247
Document Title Hattendorff’s theorem and Thiele’s differential equation generalized
Degree MSc (Actuarial Science)
Department Insurance and Actuarial Science
Supervisor
Advisor Name Title
Prof J Swart
Keywords
  • stochastic processes
  • point processes
  • Lebesgue-Stieltjes integration
  • discounting
  • Hattendorff’s theorem
  • Thiele’s differential equation
Date 2005-02-17
Availability unrestricted
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.

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