Physical Extinction and Long-Run Pricing under Time-Varying Beliefs

Battle Count: 53

The paper is primarily theoretical and does not propose trading strategies. However, it has indirect relevance for quantitative fixed-income trading: (1) It shows that long yields can exist without convergence of valuation weights, meaning yield-based signals may miss important maturity-dependent pricing effects. (2) The distinction between total and net disagreement provides a framework for understanding when belief-driven mispricing in bonds is persistent vs. transient. (3) The finite-maturity error bounds and exact formulas for gamma=1 could inform model risk assessment in long-dated bond pricing. (4) The alternating belief paths model procyclical expectations relevant to macro-driven trading. Overall, the contribution is more foundational/academic than directly actionable for trading systems.

The theoretical framework requires advanced knowledge of stochastic calculus (Girsanov theorem, Dambis-Dubins-Schwarz theorem, martingale theory), general equilibrium theory, and functional analysis (eigenfunction relations, total variation convergence). The numerical illustrations for gamma=1 are tractable with closed-form solutions, but general gamma requires the error bounds and approximation framework. Implementing the Hansen-Scheinkman factorization and forward measure convergence tests would require significant mathematical sophistication. No code is provided.

The paper is primarily theoretical with complete mathematical proofs. Numerical illustrations (Figure 1, Table 1) use specified parameter values (s0=5%, rho=2%, sigma=15%, L=20 years, omega=2pi/L) and closed-form solutions for gamma=1, making them reproducible. However, no code repository is provided. The analytical framework is fully self-contained with all formulas derived explicitly.