A review of the Markov model of life insurance with a view to surplus

Oytun Haçarız; Torsten Kleinow; Angus S. Macdonald

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arXiv · 2509.00011

A review of the Markov model of life insurance with a view to surplus

Oytun Haçarız·Torsten Kleinow·Angus S. Macdonald

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Abstract

We review Markov models of surplus in life insurance based on a counting process following Norberg (1991), uniting probabilistic theory with elements of practice largely drawn from UK experience. First, we organize models systematically based on one and two technical bases, including a suitable descriptive notation. Extending this to three technical bases to accommodate different valuation approaches leads us: (a) to expand the definition of 'technical basis' to include non-contractual cashflows recognized in the associated Thiele equation; and (b) to add new (mainly) systematic terms to the surplus. Making these cashflows dynamic or 'quasi-contractual' covers many real applications, and we give two as examples, the paid-up valuation principle and reversionary bonus on participating contracts.

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Oytun Haçarız, Torsten Kleinow, Angus S. Macdonald. 2025-08-15. A review of the Markov model of life insurance with a view to surplus. https://arxiv.org/abs/2509.00011

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