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A Simple Counterexample to Several Problems in the Theory of Asset Pricing
Author(s) -
Delbaen Freddy,
Schachermayer Walter
Publication year - 1998
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00041
Subject(s) - counterexample , integrable system , mathematical finance , martingale (probability theory) , mathematical economics , simple (philosophy) , local martingale , mathematics , martingale pricing , economics , pure mathematics , financial economics , discrete mathematics , philosophy , epistemology
We give an easy example of two strictly positive local martingales that fail to be uniformly integrable, but such that their product is a uniformly integrable martingale. The example simplifies an earlier example given by the second author. We give applications in mathematical finance and we show that the phenomenon is present in many incomplete markets.