Several transactions taking place in financial markets are dependent on the pricing of mortgages (loans for the purchase of residences, land or farms). In this article, a method for stabilization of mortgage price dynamics is developed. It is considered that mortgage prices follow a PDE model which is equivalent to a multi-asset Black-Scholes PDE. Actually it is a diffusion process evolving in a 2D assets space, where the first asset is the house price and the second asset is the interest rate. By applying semi-discretization and a finite differences scheme this multi-asset PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For the local subsystems, into which the mortgage PDE is decomposed, it becomes possible to apply boundary-based feedback control. The controller design proceeds by showing that the state-space model of the mortgage price PDE stands for a differentially flat system. Next, for each subsystem which is related to a nonlinear ODE, a virtual control input is computed, that can invert the subsystem’s dynamics and can eliminate the subsystem’s tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the multi-factor mortgage price PDE system is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the mortgage price PDE system so as to assure that all its state variables will converge to the desirable setpoints. By showing the feasibility of such a control method it is also proven that through selected modification of the PDE boundary conditions the price of the mortgage can be made to converge and stabilize at specific reference values.
Skip Nav Destination
Article navigation
28 November 2017
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2017 (ICCMSE-2017)
21–25 April 2017
Thessaloniki, Greece
Research Article|
November 28 2017
A boundary PDE feedback control approach for the stabilization of mortgage price dynamics
G. Rigatos;
G. Rigatos
*
Unit of Industrial Automation, Industrial Systems Institute
, 26504, Rion Patras, Greece
, email: [email protected]
Search for other works by this author on:
P. Siano;
P. Siano
†
Department of Industrial Engineering, University of Salerno
, Fisciano 84084 Italy
, email: [email protected]
Search for other works by this author on:
D. Sarno
D. Sarno
**
Department of Industrial Engineering, University of Salerno
, Fisciano 84084 Italy
, email: [email protected]
Search for other works by this author on:
AIP Conf. Proc. 1906, 060006 (2017)
Citation
G. Rigatos, P. Siano, D. Sarno; A boundary PDE feedback control approach for the stabilization of mortgage price dynamics. AIP Conf. Proc. 28 November 2017; 1906 (1): 060006. https://doi.org/10.1063/1.5012324
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
25
Views
Citing articles via
Inkjet- and flextrail-printing of silicon polymer-based inks for local passivating contacts
Zohreh Kiaee, Andreas Lösel, et al.
Design of a 100 MW solar power plant on wetland in Bangladesh
Apu Kowsar, Sumon Chandra Debnath, et al.
Effect of coupling agent type on the self-cleaning and anti-reflective behaviour of advance nanocoating for PV panels application
Taha Tareq Mohammed, Hadia Kadhim Judran, et al.
Related Content
Mathematical model in Islamic mortgage financing with murabahah and musharakah mutanaqisah contracts
AIP Conf. Proc. (December 2022)
The computation of dynamic fractional difference parameter for S&P500 index
AIP Conf. Proc. (October 2015)
Advanced stochastic approaches for option pricing based on Sobol sequence
AIP Conf. Proc. (September 2022)
The author’s factor analysis of labor productivity in the construction industry of the Baikal Region
AIP Conf. Proc. (October 2023)
Systemic risk and hierarchical transitions of financial networks
Chaos (June 2017)