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

An investor may be optimistic about aggregate endowment growth at some times and pessimistic at others. The weight placed on her forecast in bond valuation can therefore vary across maturities. We study whether this maturity dependence disappears at the long end of the yield curve. In a two-investor Arrow--Debreu economy, physical extinction follows when \emph{total disagreement} grows without bound. We find that bond valuation depends on net disagreement. If \emph{net disagreement} has no limit, neither the long-forward measure nor the long bond exists. Bond yields can converge along the same belief path. The long yield alone therefore cannot reveal whether valuation weights and bond returns converge across maturities. We also obtain finite-maturity error bounds for bond prices and forward densities.