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- In the permanent race for profitability, Multinational Enterprises (MNEs) seek to reduce their production cost, their wage cost and ultimately their overall tax bill. They develop strategies to reduce their global tax liability by circulating their profit through various financial vehicles and using profitable detours to exploit differences between national corporate income tax regimes. Nowadays, measures are taken by governments to strike down aggressive tax planning. This thesis, at the boundary of applied mathematics and taxation, develops a mathematical model of the least taxed path problem when a MNE wants to repatriate a profit from a source to a destination country. The flow can circulate in the form of three different vehicles, namely interests, dividends and royalties, with change of vehicle permitted in any country on the path. The model is then extended to comply with selected anti-avoidance rules and we emphasise the need for transparency. It shows that thin-capitalization rules combined with transparency are able to reduce Base Erosion and Profit Shifting (BEPS). Based on these models, two measures of BEPS are provided, one focusing on the source country and the other looking from a global point of view.