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 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 no-arbitrage. Under a sharp dichotomy condition, we prove (RLNA). Since no-one-period-arbitrage is necessary for no-arbitrage, the latter is sandwiched between two local conditions, which allows us to estimate its non-locality. Furthermore, we construct a stock price process such that two long positions in the same stock hedge each other. This puzzling phenomenon that cannot occur in arbitrage-free frictionless markets (or markets with proportional transaction costs) is used to show that no-arbitrage alone does not imply the existence of an equivalent separating measure if the probability space is infinite. Finally, we show that the model with a linear tax on capital gains can be written as a model with proportional transaction costs by introducing several fictitious securities.
Arbitrage Capital gains taxes Deferment of taxes Proportional transaction costs
Mathematics Subject Classification
This is a preview of subscription content, log in to check access.
Auerbach, A., Bradford, D.: Generalized cash-flow taxation. J. Public Econ. 88, 957–980 (2004)CrossRefGoogle Scholar
Ben Tahar, I., Soner, M., Touzi, N.: The dynamic programming equation for the problem of optimal investment under capital gains taxes. SIAM J. Control Optim. 46, 1779–1801 (2007)MathSciNetCrossRefGoogle Scholar