Premium
SHADOW PRICES FOR CONTINUOUS PROCESSES
Author(s) -
Czichowsky Christoph,
Schachermayer Walter,
Yang Junjian
Publication year - 2017
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/mafi.12103
Subject(s) - utility maximization problem , transaction cost , economics , utility maximization , shadow price , counterexample , profit (economics) , profit maximization , market price , bounded function , database transaction , microeconomics , expected utility hypothesis , mathematical economics , econometrics , mathematics , mathematical optimization , computer science , mathematical analysis , discrete mathematics , programming language
In a financial market with a continuous price process and proportional transaction costs, we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e., a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredients are the continuity of the price process and the hypothesis of “no unbounded profit with bounded risk.” A counterexample reveals that these hypotheses cannot be relaxed.