Compensation-based risk-sharing

Battle Count: 68

This paper is primarily an actuarial mathematics paper focused on insurance risk-sharing mechanisms. While it touches on capital markets (active administrator as capacity provider, insurance-linked securities reference), its core contribution is in insurance/tontine fund design rather than trading strategies. The mathematical tools (mutual exclusivity, order statistics, Dirichlet/Beta distributions) have tangential relevance to quantitative finance but the paper does not address trading, portfolio construction, or market microstructure.

The theoretical framework involves advanced probability theory, actuarial mathematics, and utility theory. Implementing the RS rules requires solving systems of nonlinear equations for actuarial fairness conditions. The Gamma/Dirichlet/Beta distributional results (Example 5, 11) provide closed-form solutions that are computationally tractable. However, for general loss distributions, numerical methods would be needed. No code is provided. The mathematical sophistication is moderate-to-high for practitioners.

The paper is purely theoretical with complete mathematical derivations, definitions, propositions, and proofs. All results are in closed form or expressed as systems of equations. Examples 1-14 provide worked numerical illustrations. No empirical data or code is required. The mathematical framework is fully self-contained with clear notation. Reproducibility is high for anyone with actuarial/mathematical background, though no computational code is provided.