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In frictionless financial markets, no-arbitrage is a local property in time.This means that a discrete time model is arbitrage-free if and only if theredoes not exist a one-period-arbitrage. With capital gains taxes, thisequivalence fails. For a model with a linear tax and one non-shortable riskystock, we introduce the concept of robust local no-arbitrage (RLNA) as theweakest local condition which guarantees dynamic no-arbitrage. Under a sharpdichotomy condition, we prove (RLNA). Since no-one-period-arbitrage isnecessary for no-arbitrage, the latter is sandwiched between two localconditions, which allows us to estimate its non-locality.  Furthermore, we construct a stock price process such that two long positionsin the same stock hedge each other. This puzzling phenomenon that cannot occurin arbitrage-free frictionless markets (or markets with proportionaltransaction costs) is used to show that no-arbitrage alone does not imply theexistence of an equivalent separating measure if the probability space isinfinite.  Finally, we show that the model with a linear tax on capital gains can bewritten as a model with proportional transaction costs by introducing severalfictitious securities.

How local in time is the no-arbitrage property under capital gains taxes ?