Please use this identifier to cite or link to this item: https://hdl.handle.net/10321/2304
Title: The algebraic properties of the space- and time-dependent one-factor model of commodities
Authors: Paliathanasis, Andronikos 
Morris, Richard M. 
Leach, P. G. L. 
Keywords: Lie point symmetries;One-factor model;Prices of commodities
Issue Date: 6-Jun-2016
Publisher: Taylor and Fancis
Source: Paliathanasis, A.; Morris, R. M. and Leach, P. G. L. 2016. The algebraic properties of the space- and time-dependent one-factor model of commodities. Quaestiones Mathematicae. 1-15.
Journal: Quaestiones mathematicae (Grahamstown. Online) 
Abstract: 
We consider the one-factor model of commodities for which the parameters of the model depend upon the stock price or on the time. For that model we study the existence of group-invariant transformations. When the parameters are constant, the one-factor model is maximally symmetric. That also holds for the time-dependent problem. However, in the case for which the parameters depend upon the stock price (space) the one-factor model looses the group invariants. For specific functional forms of the parameters the model admits other possible Lie algebras. In each case we determine the conditions which the parameters should satisfy in order for the equation to admit Lie point symmetries. Some applications are given and we show which should be the precise relation amongst the parameters of the model in order for the equation to be maximally symmetric. Finally we discuss some modifications of the initial conditions in the case of the space-dependent model. We do that by using geometric techniques.
URI: http://hdl.handle.net/10321/2304
ISSN: 1607-3606 (print)
1727-933X (online)
DOI: 10.2989/16073606.2017.1280709
Appears in Collections:Research Publications (Applied Sciences)

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