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On Azéma-Yor processes, their optimal properties and the Bachelier-drawdown equation

Abstract:

We study the class of Az\'ema-Yor processes defined from a general semimartingale with a continuous running maximum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the drawdown equation. Solutions of the latter have the drawdown property: they always stay above a given function of their past maximum. We then show that any process which satisfies the drawdown property is in fact an Az\'ema-Yor process...

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Publisher copy:
10.1214/10-AOP614
Journal:
Annals of Probability More from this journal
Volume:
40
Issue:
1
Pages:
372-400
Publication date:
2009-02-09
DOI:
ISSN:
0091-1798
Keywords:
Pubs id:
pubs:189139
UUID:
uuid:fcaabcab-e63e-4c39-85b1-05025669086b
Local pid:
pubs:189139
Source identifiers:
189139
Deposit date:
2012-12-19

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