Stabilization of the Multi-asset Black–Scholes PDE Using Differential Flatness Theory

2017 ◽  
pp. 253-263
Author(s):  
Gerasimos G. Rigatos
Keyword(s):  
Differential Flatness ◽  
Differential Flatness Theory ◽  
Black Scholes

Distributed Parameter Systems Control and Its Applications to Financial Engineering

2018 ◽  
pp. 15-35
Author(s):  
Gerasimos Rigatos ◽  
Pierluigi Siano
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Option Price ◽  
Distributed Parameter ◽  
Specific Reference ◽  
Differential Flatness ◽  
Differential Flatness Theory ◽  
Financial Model ◽  
Performance Indexes ◽  
Black Scholes

The chapter analyzes differential flatness theory for the control of single asset and multi-asset option price dynamics, described by PDE models. Through these control methods, stabilization of distributed parameter (PDE modelled) financial systems is achieved and convergence to specific financial performance indexes is made possible. The main financial model used in the chapter is the Black-Scholes PDE. By applying semi-discretization and a finite differences scheme the single-asset (equivalently multi-asset) Black-Scholes PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For this set of differential equations it is shown that differential flatness properties hold. This enables to solve the associated control problem and to stabilize the options' dynamics. By showing the feasibility of control of the single-asset (equivalently multi-asset) Black-Scholes PDE it is proven that through selected purchases and sales during the trading procedure, the price of options can be made to converge and stabilize at specific reference values.

Distributed Parameter Systems Control and Its Applications to Financial Engineering

2019 ◽  
pp. 17-45
Author(s):  
Gerasimos Rigatos ◽  
Pierluigi Siano
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
State Space Model ◽  
Option Price ◽  
Distributed Parameter ◽  
Specific Reference ◽  
Differential Flatness ◽  
Differential Flatness Theory ◽  
Financial Model ◽  
Black Scholes

The chapter analyzes differential flatness theory for the control of single asset and multi-asset option price dynamics, described by PDE models. Through these control methods, stabilization of distributed parameter (PDE modelled) financial systems is achieved and convergence to specific financial performance indices are made possible. The main financial model used in the chapter is the Black-Scholes PDE. By applying semi-discretization and a finite differences scheme the single-asset (equivalently multi-asset) Black-Scholes PDE is transformed into a state-space model consisting of ordinary nonlinear differential equations. For this set of differential equations, it is shown that differential flatness properties hold. This enables one to solve the associated control problem and to stabilize the options' dynamics. By showing the feasibility of control of the single-asset (equivalently multi-asset) Black-Scholes PDE, it is proven that through selected purchases and sales during the trading procedure, the price of options can be made to converge and stabilize at specific reference values.

scholarly journals Design and control of multiphase interleaved boost converters-based on differential flatness theory for PEM fuel cell multi-stack applications

2021 ◽  
Vol 124 ◽  
pp. 106346
Author(s):  
Phatiphat Thounthong ◽  
Pongsiri Mungporn ◽  
Damien Guilbert ◽  
Noureddine Takorabet ◽  
Serge Pierfederici ◽  
...  
Keyword(s):  
Fuel Cell ◽  
Pem Fuel Cell ◽  
Differential Flatness ◽  
Differential Flatness Theory ◽  
Boost Converters ◽  
And Control

Cooperative Trajectory Planning for Multi-UCAV Performing Air-to-Ground Target Attack Missions

2013 ◽  
Vol 718-720 ◽  
pp. 1329-1334 ◽  
Author(s):  
Xue Qiang Gu ◽  
Yu Zhang ◽  
Shao Fei Chen ◽  
Jing Chen
Keyword(s):  
Trajectory Planning ◽  
Differential Flatness ◽  
Planning Problem ◽  
Temporal Constraints ◽  
Differential Flatness Theory ◽  
Spline Curves ◽  
Ground Target ◽  
Planning Algorithm ◽  
Virtual Time ◽  
Unmanned Combat Aerial Vehicles

The problem of planning flight trajectories is studied for multiple unmanned combat aerial vehicles (UCAVs) performing a cooperated air-to-ground target attack (CA/GTA) mission. Several constraints including individual and cooperative constraints are modeled, and an objective function is constructed. Then, the cooperative trajectory planning problem is formulated as a cooperative trajectory optimal control problem (CTP-OCP). Moreover, in order to handle the temporal constraints, a notion of the virtual time based strategy is introduced. Afterwards, a planning algorithm based on the differential flatness theory and B-spline curves is developed to solve the CTP-OCP. Finally, the proposed approach is demonstrated using a typical CA/GTA mission scenario, and the simulation results show that the proposed approach is feasible and effective.

scholarly journals Control of DC–DC Converter and DC Motor Dynamics Using Differential Flatness Theory

2016 ◽  
Vol 2 (4) ◽  
pp. 371-380 ◽  
Author(s):  
G. Rigatos ◽  
P. Siano ◽  
P. Wira ◽  
M. Sayed-Mouchaweh
Keyword(s):  
Dc Motor ◽  
Differential Flatness ◽  
Differential Flatness Theory ◽  
Motor Dynamics
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