Linear vector optimization and european option pricing under proportional transaction costs

Abstract

A method for pricing and superhedging European options under proportional transaction costs based on linear vector optimisation and geometric duality developed by Löhne and Rudloff (Int. J. Theor. Appl. Finance 17(2): 1450012–1–1450012–33, 2014) is compared to a special case of the algorithms for American type derivatives due to Roux and Zastawniak (Acta Applicandae Mathematicae, published online 2015). An equivalence between these two approaches is established by means of a general result linking the support function of the upper image of a linear vector optimisation problem with the lower image of the dual linear optimisation problem.