On modelling long term stock returns with ergodic diffusion processes: arbitrage and arbitrage-free specifications
type: Item
instance of: scholarly article
title: On modelling long term stock returns with ergodic diffusion processes: arbitrage and arbitrage-free specifications
zbMATH Open document ID: 1176.62103
DOI: 10.1155/2009/215817
author: Bernard Wong
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2009-11-23T00:00:00Z
full work available at URL: https://eudml.org/doc/231448
review text: Summary: We investigate the arbitrage-free property of stock price models where the local martingale component is based on an ergodic diffusion with a specified stationary distribution. These models are particularly useful for long horizon asset-liability management as they allow the modelling of long term stock returns with heavy tail ergodic diffusions, with tractable, time homogeneous dynamics, and which moreover admit a complete financial market, leading to unique pricing and hedging strategies. Unfortunately the standard specifications of these models in the literature admit arbitrage opportunities. We investigate in detail the features of the existing model specifications which create these arbitrage opportunities and consequently construct a modification that is arbitrage free.
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 91G80
zbMATH DE Number: 5637166
Wikidata QID: Q58648155
MaRDI profile type: Publication
OpenAlex ID: W3122009644
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description: scientific article; zbMATH DE number 5637166