Pricing without no-arbitrage condition in discrete time

Laurence Carassus , Emmanuel Lépinette (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In a discrete time setting, we study the central problem of giving a fair price to some financial product. This problem has been mostly treated using martingale measures and no-arbitrage conditions. We propose a different approach based on convex duality instead of martingale measures duality: The prices are expressed using Fenchel conjugate and bi-conjugate without using any no-arbitrage condition. The super-hedging problem resolution leads endogenously to a weak no-arbitrage condition called Absence of Instantaneous Profit (AIP) under which prices are finite. We study this condition in detail, propose several characterizations and compare it to the usual no-arbitrage condition NA. Keywords Financial market models • Super-hedging prices • AIP condition • Conditional support • Essential supremum.

Domaines: Probabilités [math.PR]

Laurence Carassus, Emmanuel Lépinette. Pricing without no-arbitrage condition in discrete time. Journal of Mathematical Analysis and Applications, 2022, ⟨10.1016/j.jmaa.2021.125441⟩. ⟨hal-03283767⟩