Scaling Limits for Exponential Hedging in Trinomial Models

Battle Count: 83

The paper provides a rigorous theoretical foundation for understanding how utility-based hedging in discrete incomplete markets converges to continuous-time volatility control problems. While primarily theoretical, the results have direct implications for: (1) understanding the limits of delta-hedging in practice, (2) quantifying the cost of model incompleteness, (3) designing hedging strategies that interpolate between Black-Scholes and super-replication, and (4) calibrating models using entropy-based divergences. The asymptotic optimality of delta hedging for Markovian payoffs is practically relevant for options desks.

The paper is highly theoretical and requires advanced knowledge of stochastic analysis, martingale theory, weak convergence, optimal control, and PDE theory (HJB equations, viscosity solutions, Schauder estimates). There is no computational implementation provided. Reproducing the theoretical results requires deep mathematical expertise. Practical implementation of the delta-hedging strategy (Theorem 4.6) would require solving the nonlinear PDE (4.1) numerically, which itself is non-trivial due to the fully nonlinear structure.

The paper is entirely theoretical with complete mathematical proofs. All results are derived from first principles with explicit assumptions, definitions, and step-by-step proofs. No empirical data or code is required for verification. The mathematical arguments are self-contained and can be independently verified by experts in stochastic analysis and mathematical finance.