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|Author(s):||Alena Henclova, Charles University Prague||Title:||Notes on free lunch in the limit and pricing by conjugate duality theory|
|Date of Acceptance:||11.04.2005|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Complete Preprint:||pdf (urn:nbn:de:kobv:11-10059692)|
|Keywords (eng):||incomplete markets, free lunch, fundamental theorem of asset pricing, arbitrage pricing, conjugate duality, free lunch in the limit, multistage stochastic programming, finitelyadditive measures|
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|King and Korf introduced, in the framework of a discrete-time dynamic market model on a general probability space, a new concept of arbitrage called free lunch in the limit which is slightly weaker than the common free lunch. The definition was motivated by the attempt at proposing the pricing theory based on the theory of conjugate duality in optimization. We show that this concept of arbitrage fails to have a basic property of other common concepts used in pricing theory-it depends on the underlying probability measure more than through its null sets. However, we show that the interesting pricing results obtained by conjugate duality are still valid if it is only assumed that the market admits no free lunch rather than no free lunch in the limit. King A., Korf L., Martingale pricing measures in incomplete markets via stochastic programming duality in the dual of L1, SPEPS, 2001-13 (available at http://dochost.rz.hu-berlin.de/speps).|
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