Pricing without no-arbitrage condition in discrete time
| Autor: | Laurence Carassus, Emmanuel Lépinette |
|---|---|
| Přispěvatelé: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Computer Science::Computer Science and Game Theory
Profit (accounting) Applied Mathematics 010102 general mathematics Mathematics::Optimization and Control Duality (optimization) Mathematical Finance (q-fin.MF) 01 natural sciences FOS: Economics and business 010101 applied mathematics [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 60G44 G11-G13 Discrete time and continuous time Mathematics::Probability Quantitative Finance - Mathematical Finance Computer Science::Computational Engineering Finance and Science Fair value Product (mathematics) Applied mathematics Arbitrage 0101 mathematics Convex conjugate Martingale (probability theory) Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications Journal of Mathematical Analysis and Applications, Elsevier, In press |
| ISSN: | 0022-247X 1096-0813 |
| Popis: | In a discrete time setting, we study the central problem of giving a fair price to some financial product. For several decades, the no-arbitrage conditions and the martingale measures have played a major role for solving this problem. We propose a new approach for estimating the super-replication cost 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 details, propose several characterizations and compare it to the no-arbitrage condition. arXiv admin note: text overlap with arXiv:1807.04612 |
| Databáze: | OpenAIRE |
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