[Turkmath:8011] Doğuş University Mathematics Seminars: Ahmet Duran, Asst. Professor of Mathematics at ITU, 15:00 H-BLOK 603

[Turker Ozsari]

*Mathematics Seminars
*


**

Ahmet Duran, Asst. Professor of Mathematics at Istanbul Technical
University, will give a talk on Asset Flow Differential Equations ,
equations, to be held on Friday, Nov 18th by the Doğuş University
Mathematics Department.  His talk titled *"**Stability Analysis of Asset
Flow Differential Equations**"* will commence at 15:00.  The seminar, set
from 15:00 to 16:00 taking place at H-Block 603, will also include
refreshments afterward.


 *Title*

*Stability Analysis of Asset Flow Differential Equations*

*Speaker*


**

*Dr. Ahmet Duran,** Istanbul Technical University*


 *Location and Time*

*Doğuş University, H-Blok 603, 18 Nov, 15:00*


**

*Abstract
*
*Asset flow differential equations (AFDEs) have been developed and analyzed
asymptotically by Caginalp and collaborators since 1989 (see Caginalp and
Balenovich, Phil. Trans. R. Soc 1999; Caginalp and Ermentrout, Applied
Mathematics Letters 1991; and references contained therein). This important
mathematical model may explain various nonlinear behaviors such as
overreaction, momentum, bubbles, and crashes in experimental asset markets
and real financial markets (see Caginalp, Porter, and Smith, J. Psychol.
Finan. Mark. 2000). It incorporates several motivations for buying or
selling stock with the finiteness of assets and microeconomic principles.

It is important to understand and classify the behavior of solutions for
the dynamical system of nonlinear differential equations. This is more
challenging for dimension n ≥ 3. I studied the stability analysis of
the solutions for the dynamical system of nonlinear AFDEs in R^4, in three
versions, analytically and numerically (see Duran, Applied Mathematics
Letters, 2011). I found the existence of the infinitely many fixed points
for the first two versions. I concluded that these versions of AFDEs are
structurally unstable systems mathematically by using an extension of the
Peixoto Theorem for two-dimensional manifolds to a four dimensional
manifold. Moreover, I found that there is no critical point if the chronic
discount over the past finite time interval is nonzero for the third
version of AFDEs.

It is crucial to analyze the sources of ill-posedness in mathematical
modeling. I showed that the existence of multiple roots and that of
non-isolated roots are sources of the ill-posedness for the first two
versions of AFDEs (see Duran, Applied Mathematics Letters, 2011). I
illustrated how to reformulate the problem in order to eliminate any
hypersensitivity in the mathematical model. I introduced illustrative
examples where analytical and numerical results
seem to conflict each other and showed how to reconcile them. The analysis
in this work is important for parameter optimization of the related
dynamical system of differential equations and exception handling.
Moreover, arbitrary perturbations in numerical computation may lead to
ill-posedness, especially for such highly nonlinear dynamical systems.
Therefore, I suggest using financially meaningful optimal or feasible
parameter vectors rather than arbitrary choices. They can be obtained by
using nonlinear least-square curve fitting without overfitting (for
example, see Duran and Caginalp 2008).*




Asst. Prof. Türker Özsarı



Deparment of Mathematics

Doğuş University

Kadıköy, İstanbul

Phone: +902165445555/1688
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