NDLI: How non-arbitrage, viability and numéraire portfolio are related

Content Provider	Springer Nature Link
Author	Choulli, Tahir Deng, Jun Ma, Junfeng
Copyright Year	2015
Abstract	This paper proposes two approaches that quantify the exact relationship among viability, absence of arbitrage, and/or existence of the numéraire portfolio under minimal assumptions and for general continuous-time market models. Precisely, our first and principal contribution proves the equivalence between the no-unbounded-profit-with-bounded-risk condition (NUPBR hereafter), the existence of the numéraire portfolio, and the existence of the optimal portfolio under an equivalent probability measure for any “nice” utility and positive initial capital. Herein, a “nice” utility is any smooth von Neumann–Morgenstern utility satisfying Inada’s conditions and the elasticity assumptions of Kramkov and Schachermayer. Furthermore, the equivalent probability measure—under which the utility maximization problems have solutions—can be chosen as close to the real-world probability measure as we want (but might not be equal). Without changing the underlying probability measure and under mild assumptions, our second contribution proves that NUPBR is equivalent to the “local” existence of the optimal portfolio. This constitutes an alternative to the first contribution, if one insists on working under the real-world probability. These two contributions lead naturally to new types of viability that we call weak and local viabilities.
Ending Page	741
Page Count	23
Starting Page	719
File Format	PDF
ISSN	09492984
e-ISSN	14321122
Journal	Finance and Stochastics
Issue Number	4
Volume Number	19
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2015-07-15
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Portfolio theory Martingales and classical analysis Finance Logarithmic utility Economic Theory/Quantitative Economics/Mathematical Methods Utility maximization Probability Theory and Stochastic Processes Martingale densities Semimartingales Generalizations of martingales Quantitative Finance Stochastic integrals Non-arbitrage Utility theory Statistics for Business/Economics/Mathematical Finance/Insurance Numéraire portfolio Market viability
Content Type	Text
Resource Type	Article
Subject	Finance Statistics and Probability Statistics, Probability and Uncertainty

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