On Technical Bases and Surplus in Life Insurance

Paper: arXiv 2310.16927

Authors: Oytun Haçarız, Torsten Kleinow, Angus S. Macdonald

Abstract

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 (1988a). We conclude with two applications: lapse-supported business; and the retrospectively-oriented regime proposed by Møller & Steffensen (2007).

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical generalization of Thiele’s differential equations and surplus modeling in life insurance via Markov processes. While highly novel and theoretically complete, it lacks empirical validation, real-world backtests, or datasets.

Research Flowchart

  flowchart TD
    A["Research Goal: Revisit & generalize surplus theory via Markov models & Thiele's equations"] --> B["Input: Markov Chain Models & 4 Technical Bases<br/>(Premium, Valuation, Accumulation, Real-World)"]
    B --> C["Methodology: Formulate boundary conditions for Thiele's differential equations"]
    C --> D["Analysis: Derive premium loadings & surplus from pairs of technical bases"]
    D --> E["Applications: Evaluate lapse-supported business & Møller-Steffensen regime"]
    E --> F["Outcome: Generalized surplus framework expanding Ramlau-Hansen results"]