Notes on free lunch in the limit and pricing by conjugate duality theory

Alena Henclová

Kybernetika (2006)

  • Volume: 42, Issue: 1, page 57-76
  • ISSN: 0023-5954

Abstract

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King and Korf [KingKorf01] 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.

How to cite

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Henclová, Alena. "Notes on free lunch in the limit and pricing by conjugate duality theory." Kybernetika 42.1 (2006): 57-76. <http://eudml.org/doc/33792>.

@article{Henclová2006,
abstract = {King and Korf [KingKorf01] 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.},
author = {Henclová, Alena},
journal = {Kybernetika},
keywords = {free lunch; free lunch in the limit; fundamental theorem of asset pricing; incomplete markets; arbitrage pricing; multistage stochastic programming; conjugate duality; finitely-additive measures; free lunch; asset pricing; incomplete markets; arbitrage pricing; conjugate duality; finitely-additive measures},
language = {eng},
number = {1},
pages = {57-76},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Notes on free lunch in the limit and pricing by conjugate duality theory},
url = {http://eudml.org/doc/33792},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Henclová, Alena
TI - Notes on free lunch in the limit and pricing by conjugate duality theory
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 1
SP - 57
EP - 76
AB - King and Korf [KingKorf01] 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.
LA - eng
KW - free lunch; free lunch in the limit; fundamental theorem of asset pricing; incomplete markets; arbitrage pricing; multistage stochastic programming; conjugate duality; finitely-additive measures; free lunch; asset pricing; incomplete markets; arbitrage pricing; conjugate duality; finitely-additive measures
UR - http://eudml.org/doc/33792
ER -

References

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