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INVARIANT APPROACHES FOR THE ANALYTIC SOLUTION OF THE STOCHASTIC BLACK-DERMAN TOY MODEL

ABSTRACT
We work on the analytical solution of the stochastic differential equations (SDE) via invariant approaches. In particularly, we focus on the stochastic Black-Derman Toy (BDT) interest rate model, among others. After we present corresponding (1+1) parabolic linear PDE for BDT-SDE, we use theoretical framework about the invariant approaches for the (1+1) linear PDE being done in the literature. We show that it is not possible to reduce BDT-PDE into the first and second Lie canonical forms. On the other hand, we success to find transformations for reducing it to the third Lie canonical form. After that, we obtain analytical solution of BDT-PDE by using these transformations. Moreover, we conclude that it can be reduced to the fourth Lie canonical form but, to the best of our knowledge, its analytical solution in this form is hard to find yet.
KEYWORDS
PAPER SUBMITTED: 2017-11-20
PAPER REVISED: 2017-12-25
PAPER ACCEPTED: 2018-01-10
PUBLISHED ONLINE: 2018-02-18
DOI REFERENCE: https://doi.org/10.2298/TSCI171120030I
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S265 - S275]
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© 2018 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence