Additive portfolio improvement and utility-efficient payoffs
type: Item
instance of: scholarly article
title: Additive portfolio improvement and utility-efficient payoffs
zbMATH Open document ID: 1369.91163
author: Stefan Kassberger
author: Thomas Liebmann
published in: Mathematics and Financial Economics
publication date: 2017-03-07T00:00:00Z
review text: This paper studies the notion of \textit{amelioration} (or additive improvement procedure) of payoffs. More specifically, an amelioration is a function \(A:L^1(\Omega,\mathcal{F},\mathbb{P})\rightarrow L^1(\Omega,\mathcal{F},\mathbb{P})\) satisfying: {\parindent=0.7cm\begin{itemize}\item[(1)] \(A(X+Y)=A(X)+A(Y)\); \item[(2)] \(X\geq c \Longrightarrow A(X)\geq c\), for all constants \(c\); \item[(3)] \(A(A(X))=A(X)\); \item[(4)] \(\mathbb{E}[A(X)^-]\leq\mathbb{E}[X^-]\). \end{itemize}} The additivity requirement has the important implication that \(A(-X)=-A(X)\), thus implying that both the seller and the buyer of \(X\) would agree on replacing \(X\) with its amelioration \(A(X)\). The authors prove that a function \(A\) is an amelioration if and only if it is a conditional expectation operator. Moreover, it is shown that ameliorations are the only additive improvement procedures that improve payoffs for every expected utility maximizer. Specific ameliorations can be chosen to achieve consistency with the pricing measure and with utility maximization. In general, an amelioration does not preserve the distribution of a payoff, but is consistent with risk-averse robust Savage preferences. Finally, the authors prove that an ameliorated payoff cannot represent a statistical arbitrage opportunity.
reviewed by: Claudio Fontana
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 6692622
zbMATH Keywords: payoff improvement
zbMATH Keywords: additive
zbMATH Keywords: conditional expectation
zbMATH Keywords: uniform preferences
zbMATH Keywords: robust Savage utility
MaRDI profile type: Publication
full work available at URL: s11579-016-0179-3
OpenAlex ID: W2519523186
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DOI: 10.1007/S11579-016-0179-3
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description: scientific article; zbMATH DE number 6692622