
Arbitrage and completeness in financial markets with given N-dimensional distributions
Campi, Luciano, Arbitrage and completeness in financial markets with given N-dimensional distributions, Decisions in Economics and Finance;1593-8883, 27, 1, p. 57–80. 10.1007/s10203-004-0044-3
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Article accepté pour publication ou publiéJournal name
Decisions in Economics and Finance;1593-8883Volume
27Number
1Publisher
Springer
Pages
57–80
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Campi, LucianoCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Laboratoire de Finance des Marchés d'Energie [FiME Lab]
Abstract (EN)
In this paper, we focus on the following problem: given a financial market, modelled by a process S=(St)t∈T, and a family MN={μt1,…,tN:t1,…,tN∈T} of probability measures on B(RN), with N a positive integer and T the time space, we search for financially meaningful conditions which are equivalent to the existence and uniqueness of an equivalent (local) martingale measure (EMM) Q such that the price process S has under Q the pre-specified finite-dimensional distributions of order N (N-dds) MN. We call these two equivalent properties, respectively, N -mixed no free lunch and market N -completeness. They are based on a classification of contingent claims with respect to their path-dependence on S and on the related notion of N-mixed strategy. Finally, we apply this approach to the Black-Scholes model with jumps, by showing a uniqueness result for its equivalent martingale measures set.Subjects / Keywords
Price Process; Risky Asset; Trading Strategy; Option Price; Probability MeasureRelated items
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