In these notes, we introduce the theory of arbitrage and pricing for frictionless models, i.e. the classical theory of mathematical finance. The main classical results are presented, namely the characterization of absence of arbitrage opportunities, based on convex duality. Dual characterizations of super-hedging prices are deduced. We then introduce financial market models with proportional transaction costs. We discuss no arbitrage conditions and characterize super-hedging prices as in the frictionless case. An alternative approach based on the liquidation value concept is finally presented.
The following lectures have been written for the workshop organized from Monday the 22th to the 26th of April 2019 by the laboratory Latao of the Faculty of Sciences of Tunis and by the reasearch group Gosaef which gathers researchers working on order structures, mathematical finance and mathematical economics. These notes are devoted to graduate students and anyone who wants to be initiated to arbitrage theory. The author thanks the organizers, in particular Amine Ben Amor for his hearty welcome.
Received: May 11, 2019
Published online: August 1, 2019
Emmanuel LepinetteParis Dauphine university, PSL research university, Cérémade, CNRS, UMR, Place du Maréchal De Lattre De Tassigny, 75775 Paris cedex 16, France.