Borch's theorem from the perspective of comonotonicity
type: Item
instance of: scholarly article
title: Borch's theorem from the perspective of comonotonicity
zbMATH Open document ID: 1403.91191
author: K. C. Cheung
author: Yian Rong
author: Sheung Chi Phillip Yam
published in: Insurance Mathematics \& Economics
publication date: 2014-06-23T00:00:00Z
review text: The paper deals with Borch's theorem on the characterization of Pareto optimal risk exchange treaties under the expected utility paradigm (in the framework of risk allocation the Pareto optimality means that it is impossible to improve the wellbeing of one trader without worsening the wellbeing of at least one other trader). Instead of optimizing by means of the traditional Lagrangian method or variational arguments the paper proposes a new method based on a Breeden-Litzenberger integral representation formula which allows to rewrite the objective function into a sum of mixtures of stop-loss transforms of the risk allocations. Moreover, this sum can be optimized applying the theory of comonotonicity. This approach enables e.g. to derive a closed-form expression for the given problem including the classical Borch's theorem and other interesting results.
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 6306784
zbMATH Keywords: Borch's theorem
zbMATH Keywords: comonotonicity
zbMATH Keywords: expected utility paradigm
zbMATH Keywords: optimal risk exchange
zbMATH Keywords: Pareto optimality
reviewed by: Tomáš Cipra
MaRDI profile type: Publication
full work available at URL: j.insmatheco.2013.11.006
OpenAlex ID: W2002133786
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DOI: 10.1016/J.INSMATHECO.2013.11.006
description: scientific article; zbMATH DE number 6306784