Tootfinder

A review of the Markov model of life insurance with a view to surplus
Oytun Ha\c{c}ar{\i}z, Torsten Kleinow, Angus S. Macdonald
https://arxiv.org/abs/2509.00011 https://

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

Interleaving Logic and Counting
Johan van Benthem, Thomas Icard
https://arxiv.org/abs/2507.05219 https://arxiv.org/pdf/2507.05219

Interleaving Logic and Counting
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common linguistic usage and its extension into the broader practice of natural language plus "grassroots mathematics". We begin with a brief review of first-order logic with counting operators and cardinality comparisons. This system is known to be of high complexity, and …