The numéraire portfolio in semimartingale financial models
type: Item
instance of: scholarly article
title: The numéraire portfolio in semimartingale financial models
zbMATH Open document ID: 1144.91019
author: Constantinos Kardaras
author: Ioannis Karatzas
published in: Finance and Stochastics
publication date: 2007-12-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/0803.1877
review text: The authors consider a general semimartingale model without further mathematical assumptions. On the economic side, it is assumed that assets have their prices determined exogenously and can be traded without ``frictions'': transaction costs are non-existent or negligible. The main concern is a problem of dynamic stochastic optimization: to find a trading strategy whose wealth appears ``better'' when compared to the wealth generated by any other strategy, in the sense that the ratio of the two processes is a supermartingale. If such a strategy exists, it is essentially unique and is called numéraire portfolio. Necessary and sufficient conditions for the numéraire portfolio to exist are derived, in terms of the triplet of predictable characteristics of the stock-price returns. A bare-hands approach is used, the assumption of finite expected log-utility is dropped entirely; no normative assumptions is imposed. It turns out that the numéraire portfolio can exist even when the classical No Arbitrage condition fails.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 5220221
zbMATH Keywords: numéraire portfolio
zbMATH Keywords: semimartingale
zbMATH Keywords: predictable characteristics
zbMATH Keywords: free lunch
zbMATH Keywords: supermartingale deflator
zbMATH Keywords: log-utility
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
OpenAlex ID: W2164288937
arXiv ID: 0803.1877
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DOI: 10.1007/S00780-007-0047-3
description: scientific article