NDLI: On the game interpretation of a shadow price process in utility maximization problems under transaction costs

Content Provider	Springer Nature Link
Author	Rokhlin, Dmitry B.
Copyright Year	2013
Abstract	To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S ∗, lying in the bid/ask price interval $[\underline{S}, \overline{S}]$ . Such a process S ∗ is called a shadow price if it provides the same optimal utility value as in the original model with bid-ask spread.We call S ∗ a generalized shadow price if the above property is true for the relaxed utility function in the frictionless model. This relaxation is defined as the lower semicontinuous envelope of the original utility, considered as a function on the set $[\underline{S}, \overline{S}]$ , equipped with some natural weak topology. We prove the existence of a generalized shadow price under rather weak assumptions and mark its relation to a saddle point of the trader/market zero-sum game, determined by the relaxed utility function. The relation of the notion of a shadow price to its generalization is illustrated by several examples. Also, we briefly discuss the interpretation of shadow prices via Lagrange duality.
Ending Page	838
Page Count	20
Starting Page	819
File Format	PDF
ISSN	09492984
e-ISSN	14321122
Journal	Finance and Stochastics
Issue Number	4
Volume Number	17
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-04-19
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Finance/Investment/Banking Portfolio theory Shadow price process Utility maximization Probability Theory and Stochastic Processes Duality Transaction costs Quantitative Finance Saddle point Utility theory for games Statistics for Business/Economics/Mathematical Finance/Insurance Economic Theory Lower semicontinuous envelope Minimax problems
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

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