2025/12/15 by Furrer, Christian, Hornung, Philipp C.
#FOS: Economics and business #FOS: Mathematics #Probability (math.PR) #Risk Management (q-fin.RM)
paper · doi:10.48550/arxiv.2512.13562
The classic semi-Markov disability model is expanded with individual and collective health claims to improve its explanatory and predictive power -- in particular in the context of group experience rating. The inclusion of collective health claims leads to a computationally challenging many-body problem. By adopting a mean-field approach, this many-body problem can be approximated by a non-linear one-body problem, which in turn leads to a transparent pricing method for disability coverages based on a lower-dimensional system of non-linear forward integro-differential equations. In a practice-oriented simulation study, the mean-field approximation clearly stands its ground in comparison to naïve Monte Carlo methods.