Determinacy and Analytical Tail Solutions in the Sequence Space

Zaichuan Du

No 2026/0434, Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa

Abstract: We develop a continuous-time geometric formulation of local equilibrium in sequence space. Household optimality, distributional transport, and market clearing define a common equilibrium relation whose linearization is an operator on admissible paths. Its kernel measures first-order indeterminacy; its cokernel identifies restrictions on shocks required for existence. Under an exponential dichotomy and a closed-range condition, we reduce both questions to the map from stable initial traces to predetermined data. The same stable–unstable decomposition yields an exact analytic boundary condition for an infinite stationary tail. Solving a finite prefix with this condition is equivalent to solving the original half-line problem and introduces no time-horizon truncation error.

Keywords: sequence-space Jacobian; determinacy; geometric closure; continuous time; analytic tails; discrete exterior calculus. (search for similar items in EconPapers)
JEL-codes: C61 C63 E21 (search for similar items in EconPapers)
Date: 2026-10
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