In this thesis, we define a new concept of duration for FX Swaps and more broadly for sovereign bonds. The con-cept of duration already exists for bonds and more specifically coupon bonds, where it is also called ”Macauley Duration”. We aim to define a concept for FX Swaps with similar financial properties and derive mathematical properties from the new definition. A major result of this thesis is the Duration Equivalence Theorem, which states that FX Swap portfolios with the same duration have roughly the same payoff and by extension similar risk exposures. This theorem can be used as a tool for portfolio management and hedging purposes. We also derive a bound of the remainder of the approximation in the theorem so that the applicability of the theorem can be assessed. Based on this first major result, the remainder of the thesis is focused on FX Swap portfolio optimization.

A study of train delay propagation using max-plus algebra and extensions of the max-plus model.