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

In frictionless financial markets, no-arbitrage is a local property in time. This means, a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage. With capital gains taxes, this... [ view full abstract ]

In frictionless financial markets, no-arbitrage is a local property in time. This means, a discrete time model is arbitrage-free if and only if there does not exist a one-period-arbitrage. With capital gains taxes, this equivalence fails. For a model with a linear tax and one non-shortable risky stock, we introduce the concept of robust local no-arbitrage (RLNA) as the weakest local condition which guarantees dynamic arbitrage-freeness. Under a sharp dichotomy condition, we prove (RLNA). Since no-one-period-arbitrage is necessary for no-arbitrage, the latter is nested between two local conditions, which allows us to estimate its non-locality.