Long-Run Sovereign Debt Composition: An Analytic Ergodic Framework with Explicit Maturity Structure

Battle Count: 75

The paper is primarily focused on sovereign debt management and fiscal policy rather than quantitative trading. However, it has indirect relevance: (1) understanding long-run debt composition informs fixed-income portfolio construction and duration management; (2) the ergodic framework and SRE methodology could inform systematic bond portfolio rebalancing; (3) rollover risk metrics are relevant for Treasury market participants; (4) the cost-risk frontier analysis parallels portfolio optimization in trading contexts. The paper does not address trading strategies, market microstructure, or short-term price dynamics.

The deterministic baseline requires linear algebra (companion matrices, Perron-Frobenius) and is straightforward to implement. The stochastic extension requires understanding of SRE theory, Foster-Lyapunov conditions, and the future-cashflow state representation. Monte Carlo simulation of the SRE is computationally simple (linear recursion). The optimization problem transitions from linear programming (deterministic) to sequential quadratic programming (stochastic). Key challenges: correctly implementing the 2M-dimensional future-cashflow state, handling the Sherman-Morrison inversion, and ensuring sufficient simulation horizon for ergodic convergence. The analytical formulas are closed-form but involve matrix operations of dimension 2M.

The paper provides complete analytical formulas, parameter tables (Tables 1-4), and simulation parameters (Table 3: 100 periods, 500 paths). However, no code repository is provided. The mathematical derivations are self-contained and reproducible given the stated assumptions. Monte Carlo simulation parameters are fully specified. The model structure is deterministic given parameters, enabling replication of analytical results. No external data is required as the model is purely parametric.