EconPapers    
Economics at your fingertips  
 

BOUNDARY CONTROL OF THE BLACK–SCHOLES PDE FOR OPTION DYNAMICS STABILIZATION

Gerasimos G. Rigatos ()
Additional contact information
Gerasimos G. Rigatos: Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece

Annals of Financial Economics (AFE), 2016, vol. 11, issue 02, 1-29

Abstract: The objective of the paper is to develop a boundary control method for the Black–Scholes PDE which describes option dynamics. It is shown that the procedure for numerical solution of Black–Scholes PDE results into a set of nonlinear ordinary differential equations (ODEs) and an associated state equations model. For the local subsystems, into which a Black–Scholes 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 Black–Scholes 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 Black–Scholes 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 Black–Scholes PDE system so as to assure that all its state variables will converge to the desirable setpoints.

Keywords: Black–Scholes PDE; options pricing; differential flatness theory; distributed parameter systems; nonlinear feedback control (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S2010495216500093
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:afexxx:v:11:y:2016:i:02:n:s2010495216500093

Ordering information: This journal article can be ordered from

Access Statistics for this article

Annals of Financial Economics (AFE) is currently edited by Michael McAleer

More articles in Annals of Financial Economics (AFE) from World Scientific Publishing Co. Pte. Ltd.
Series data maintained by Tai Tone Lim ().

 
Page updated 2017-12-16
Handle: RePEc:wsi:afexxx:v:11:y:2016:i:02:n:s2010495216500093