Option spanning with exogenous information structure

Options and efficiency in spaces of bounded claims

“…This amounts to a direct generalization of Ross' finite-dimensional spanning result for a class of L ∞ -spaces that are extremely common in the extant literature. Also, this result extends the findings of Section 3 in Galvani (2009) to L ∞ (P).…”

“…6 An element x in L ∞ (P) is called a.s. injective if it is a.s. equal to an injective function on , or, more precisely, if x has an injective representative. The following fact is an extension (with the same proof) of Lemma 2 of Galvani (2009) …”

“…Corollary 3 follows immediately from Lemma 2 and Theorem 1 in Galvani (2009). We conclude this introductory section by stating few classical facts.…”

“…See the discussion of Artzner and Heath's paradox inJarrow et al (1999).6 Because we can always make positive a claim in L∞(P) by adding a constant, in this work we do not need to treat separately the case of options with positive strike prices (c.f.,(Galvani, 2009)). …”

Maximal submarkets that replicate any option

“…In Galvani (2009), the results of Ross (1976) are studied in L p spaces. In (2006), Kountzakis and Polyrakis closed the problem of the determination of the completion by options of X by giving a complete method which determines a positive basis of F 1 (X ).…”