Optimal Underreporting and Competitive Equilibrium

Battle Count: 108

This paper is entirely focused on insurance economics and actuarial pricing under Bonus-Malus Systems. It does not address trading strategies, asset pricing, market microstructure, or any quantitative trading applications. The game-theoretic and optimization frameworks used are specific to insurance contract design and premium setting.

The theoretical framework involves solving Bellman equations on finite-state Markov chains, computing stationary distributions, and finding fixed points of best-response mappings. Numerical implementation requires: (1) computing the optimal barrier via the semi-explicit formula, (2) constructing the transition matrix for the insured's state process, (3) solving for the stationary distribution, (4) computing expected profits, and (5) iterating to find the Nash equilibrium via fixed-point methods. The 2-class restriction simplifies computation but the fixed-point iteration and sensitivity analysis require careful numerical handling.

The paper provides complete mathematical proofs in Appendix A, a concrete numerical example in Appendix B, and a full parameter table (Table 1) for the base case. All model specifications, transition probabilities, and equilibrium conditions are explicitly stated. However, no code or software implementation is provided. The numerical analysis appears to be reproducible given the stated parameters and loss distribution (Gamma mixture).