A short introduction to arbitrage theory and pricing in mathematical finance for discrete-time markets with or without friction
Lépinette, Emmanuel (2019), A short introduction to arbitrage theory and pricing in mathematical finance for discrete-time markets with or without friction, The Graduate Journal of Mathematics, 4, 1, p. 30-41
TypeArticle accepté pour publication ou publié
External document linkhttps://gradmath.org/2020/10/05/a-short-introduction-to-arbitrage-theory-and-pricing-in-mathematical-finance-for-discrete-time-markets-with-or-without-frictions/
Journal nameThe Graduate Journal of Mathematics
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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.
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