2024/11/19 by Marcus C. Christiansen, Christiansen, Marcus C., Christian Furrer +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Probability and Risk Models #Risk Management (q-fin.RM) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2411.12522
openalex publication_date 2024/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thiele's differential equation explains the change in prospective reserve and plays a fundamental role in safe-side calculations and other types of actuarial model comparisons. This paper presents a `model lean' version of Thiele's equation with the novel feature that it supports any canonical insurance model, irrespective of the model's intertemporal dependence structure. The basis for this is a canonical and path-wise model construction that simultaneously handles discrete and absolutely continuous modeling regimes. Comparison theorems for differing canonical insurance models follow directly from the resulting stochastic backward equations. The elegance with which these comparison theorems handle non-equivalence of probability measures is one of their major advantages over previous results.