Options and efficiency in spaces of bounded claims |
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Authors: | Valentina Galvani Vladimir G. Troitsky |
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Affiliation: | 1. Department of Economics, University of Alberta, Edmonton, AB, T6G 2R3, Canada;2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada |
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Abstract: | In 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 Lp-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. |
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Keywords: | C0 D61 G10 G12 G19 |
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