The theme of this thesis is duality methods in mathematical -nance. This is a hot topic in the eld of mathematical nance,and there is currently a lot of research activity regarding thissubject. However, since it is a fairly new eld of study, a lotof the material available is technical and di cult to read. Thisthesis aims to connect the duality methods used in mathematical nance to the general theory of duality methods in optimizationand convexity, and hence clarify the subject. This requires theuse of stochastic, real and functional analysis, as well as measureand integration theory.
The thesis begins with a presentation of convexity and conju-gate duality theory. Then, this theory is applied to convex riskmeasures. The nancial market is introduced, and various dualitymethods, including linear programming duality, Lagrange dualityand conjugate duality, are applied to solve utility maximization,pricing and arbitrage problems. This leads to both alternativeproofs of known results, as well as some (to my knowledge) newresults.