Minimal Solutions to the Skorokhod Reflection Problem Driven by Jump Processes and an Application to Reinsurance

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The paper is primarily focused on insurance mathematics and reinsurance, not quantitative trading. However, the Skorokhod reflection framework and jump process modeling have indirect relevance to: (1) systemic risk modeling in financial networks, (2) liquidity risk and default time estimation, (3) the mathematical machinery of reflected processes used in some option pricing models. The connection to trading strategies is minimal.

The theoretical framework requires advanced knowledge of stochastic processes, linear programming duality, and convex analysis. The LP formulation is standard and solvable via simplex method. The fixed-point iteration (Knaster-Tarski) is straightforward to implement. Monte Carlo simulation of the two-firm reinsurance model is moderate in complexity. The main challenge lies in correctly implementing the Skorokhod reflection map for jump processes and handling the dual cone condition for extension times.

The paper provides complete mathematical proofs and specifies all Monte Carlo simulation parameters (20000 trials, initial conditions, Poisson intensities, exponential claim sizes, premium rates, friction parameter). However, no code repository or supplementary computational materials are provided. The theoretical framework is fully self-contained, but numerical reproduction would require implementing the Monte Carlo simulations from scratch.