Disability Insurance with Collective Health Claims: A Mean-Field Approach

Battle Count: 67

This paper is firmly in the domain of actuarial science and insurance mathematics. While it involves stochastic processes, jump processes, and integro-differential equations that share mathematical foundations with quantitative finance, the application is specifically to disability insurance pricing and group experience rating. There is no direct relevance to trading strategies, market microstructure, or portfolio construction in financial markets.

The implementation requires solving systems of non-linear forward integro-differential equations using a meta-algorithm with Euler steps and trapezoidal integration. The mean-field framework involves chaosticity proofs, total variation convergence, and careful handling of distribution-dependent processes. The non-linearity introduces potential uniqueness issues. The numerical scheme requires discretization in time, duration, and health claim count dimensions. However, the paper provides a clear meta-algorithm (Section 4) and demonstrates feasibility in R.

The paper provides a detailed simulation study with specific parameter values (Table 1), explicit model specifications, and describes the numerical implementation (Euler method, trapezoidal rule, meta-algorithm from [3]). Code is implemented in R. However, no code repository is explicitly linked. The mathematical framework is fully specified with proofs. Convergence parameters (step length 0.0125, cut-off K_H=15) are stated.