2025/08/15 by Oytun Haçarız, Haçarız, Oytun, Torsten Kleinow +3
Decision Sciences · Mathematics · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.2509.00011
openalex publication_date 2025/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.