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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

Type
Article accepté pour publication ou publié
External document link
https://gradmath.org/2020/10/05/a-short-introduction-to-arbitrage-theory-and-pricing-in-mathematical-finance-for-discrete-time-markets-with-or-without-frictions/
Date
2019
Journal name
The Graduate Journal of Mathematics
Volume
4
Number
1
Pages
30-41
Metadata
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Author(s)
Lépinette, Emmanuel
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.