Stackelberg Equilibria in Monopoly Insurance Markets with Probability Weighting

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The paper is primarily relevant to insurance economics and actuarial science rather than quantitative trading. However, it has tangential relevance through: (1) distortion risk measures (VaR, CVaR/TVaR) are widely used in risk management for trading portfolios; (2) the game-theoretic framework could inform understanding of market microstructure in insurance-linked securities; (3) probability weighting concepts relate to behavioral finance. The direct applicability to trading strategies, portfolio optimization, or market prediction is minimal.

The theoretical framework requires advanced knowledge of: (1) game theory (Stackelberg equilibria, sequential games); (2) distortion risk measures and Choquet integration; (3) quantile function optimization; (4) comonotonicity and stochastic dominance; (5) measure-theoretic probability. The proofs involve careful case analysis of distortion function properties. Numerical implementation of the examples requires handling parametric distortion functions and computing integrals over quantile spaces. No code is provided, and the mathematical sophistication is high.

The paper is purely theoretical with complete mathematical proofs provided in appendices (A.1-A.7). All definitions, assumptions, and theorems are explicitly stated. The numerical examples in Section 5.3 use specific parametric distortion functions (Tversky-Kahneman) and loss distributions (uniform, truncated exponential, Kumaraswamy) that can be independently verified. However, no code or computational scripts are provided. The theoretical results are fully self-contained and verifiable by a reader with appropriate mathematical background.