Options and efficiency in spaces of bounded claims

Abstract

a b s t r a c tIn a seminal contribution, Ross (1976) showed that a static finite state-space market can be completed by supplementing the primitive securities with ordinary call and put options. Galvani (2009) extends this result to norm separable L p -spaces, with 1 ≤ p < ∞. This study concludes that options maintain the same spanning power in the space of bounded payoffs topologized by the duality with the space of the state price densities. In particular, under mild assumptions on the probability space, options written on a claim that is a.s. equal to an injective function complete the market.

Option spanning beyond $$L_p$$ L p -models

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The aim of this paper is to study the spanning power of options in a static financial market that allows non-integrable assets. Our findings extend and unify the results in [13,14,24] for L p -models. We also apply the spanning power properties to the pricing problem.

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Smallest order closed sublattices and option spanning

“…Through the work of Nachman [22], Galvani [9], and Galvani and Troitsky [10], it is established that, if f is of limited liability, i.e., f ≥ 0 a.s., then…”