On technical bases and surplus in life insurance

We revisit surplus on general life insurance contracts, represented by Markov models. We classify technical bases in terms of boundary conditions in Thiele's equation(s), allowing more general regulations than Scandinavian-style ‘first-order/second-order’ regimes, and replacing the traditional retrospective policy value. We propose a ‘canonical’ model with three technical bases (premium, valuation, accumulation) and show how each pair of bases defines premium loadings and surplus. Along with a ‘true’ or ‘real-world’ experience basis, this expands fundamental results of Ramlau-Hansen [(1988b). The emergence of profit in life insurance. Insurance: Mathematics and Economics, 7(4), 225–236]. We conclude with two applications: lapse-supported business; and the retrospectively-oriented regime proposed by Møller and Steffensen [(2007). Market-valuation methods in life and pension insurance. Cambridge University Press].