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dc.contributor.authorAntonopoulou, Dimitra
dc.contributor.authorBitsaki, Marina
dc.contributor.authorKarali, Georgia
dc.date.accessioned2021-03-10T11:33:46Z
dc.date.available2021-03-10T11:33:46Z
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/624340/DCDSB_accept_2021_Stoc_Stefan2012.13432.pdf?sequence=1
dc.identifier.citationAntonopoulou, D. C., Bitsaki, M., & Karali, G. (2021 - forthcoming). The multi-dimensional stochastic Stefan financial model for a portfolio of assets. Discrete & Continuous Dynamical Systems - B, https://doi.org/10.3934/dcdsb.2021118
dc.identifier.issn1531-3492
dc.identifier.doi10.3934/dcdsb.2021118
dc.identifier.urihttp://hdl.handle.net/10034/624340
dc.descriptionThis is an electronic version of an article published in [include the complete citation information for the final version of the Article as published in the print edition of the Journal.]
dc.description.abstractThe financial model proposed in this work involves the liquidation process of a portfolio of n assets through sell or (and) buy orders placed, in a logarithmic scale, at a (vectorial) price with volatility. We present the rigorous mathematical formulation of this model in a financial setting resulting to an n-dimensional outer parabolic Stefan problem with noise. The moving boundary encloses the areas of zero trading, the so-called solid phase. We will focus on a case of financial interest when one or more markets are considered. In particular, our aim is to estimate for a short time period the areas of zero trading, and their diameter which approximates the minimum of the n spreads of the portfolio assets for orders from the n limit order books of each asset respectively. In dimensions n = 3, and for zero volatility, this problem stands as a mean field model for Ostwald ripening, and has been proposed and analyzed by Niethammer in [25], and in [7] in a more general setting. There in, when the initial moving boundary consists of well separated spheres, a first order approximation system of odes had been rigorously derived for the dynamics of the interfaces and the asymptotic pro le of the solution. In our financial case, we propose a spherical moving boundaries approach where the zero trading area consists of a union of spherical domains centered at portfolios various prices, while each sphere may correspond to a different market; the relevant radii represent the half of the minimum spread. We apply It^o calculus and provide second order formal asymptotics for the stochastic version dynamics, written as a system of stochastic differential equations for the radii evolution in time. A second order approximation seems to disconnect the financial model from the large diffusion assumption for the trading density. Moreover, we solve the approximating systems numerically.en_US
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en_US
dc.relation.urlhttps://www.aimsciences.org/article/doi/10.3934/dcdsb.2021118
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.titleThe multi-dimensional Stochastic Stefan Financial Model for a portfolio of assetsen_US
dc.typeArticleen_US
dc.identifier.eissn1553-524Xen_US
dc.contributor.departmentUniversity of Chester; University of Creteen_US
dc.identifier.journalDiscrete and Continuous Dynamical Systems Ben_US
or.grant.openaccessYesen_US
rioxxterms.funderUnfundeden_US
rioxxterms.identifier.projectUnfundeden_US
rioxxterms.versionAMen_US
rioxxterms.licenseref.startdate2022-07-01
dcterms.dateAccepted2021-03-10
rioxxterms.publicationdate2021-04
dc.date.deposited2021-03-10en_US


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