Arbitrage and viability in securities markets with fixed trading costs

Elyès Jouini (1) , Hedi Kallal (2) , Clotilde Napp (1, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 SBS - salomon barney smith
3 CREST - Centre de Recherche en Économie et Statistique

This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerage fees, investment taxes, operational, and processing costs or opportunity costs. We show that the absence of free lunches in such models is equivalent to the existence of a family of absolutely continuous probability measures for which the normalized securities price processes are martingales. This is a weaker condition than the absence of free lunch in frictionless models, which is equivalent to the existence of an equivalent martingale measure. We also show that the only arbitrage-free pricing rules on the set of attainable contingent claims are those that are equal to the sum of an expected value with respect to any absolutely continuous martingale measure and of a bounded fixed cost functional. Moreover, these pricing rules are the only ones to be viable as models of economic equilibrium.

Mots clés: Arbitrage; Fixed costs; Absolutely continuous Martingale measure; Contingent claims pricing

Domaines: Economies et finances; Gestion et management; Méthodes et statistiques

Elyès Jouini, Hedi Kallal, Clotilde Napp. Arbitrage and viability in securities markets with fixed trading costs. Journal of Mathematical Economics, 2001, pp.197-221. ⟨halshs-00167157⟩