scholarly journals Optimal Liquidation Behaviour Analysis for Stochastic Linear and Nonlinear Systems of Self-Exciting Model with Decay

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jiangming Ma ◽  
Xiankang Luo
Keyword(s):  
Control Method ◽  
Variable Coefficients ◽  
Price Impact ◽  
The Self ◽  
Impact Model ◽  
Nonlinear Odes ◽  
Optimal Liquidation ◽  
Optimal Control Method ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

When the market environment changes, we extend the self-exciting price impact model and further analysis of investors’ liquidation behaviour. It is assumed that the model is accompanied by an exponential decay factor when the temporary impact and its coefficient are linear and nonlinear. Using the optimal control method, we obtain that the optimal liquidation behaviours satisfy the second-order nonlinear ODEs with variable coefficients in the case of linear and nonlinear temporary impact. Next, we solve the ODEs and get the form of the investors’ optimal liquidation behaviour in four cases. Furthermore, we prove the decreasing properties of the optimal liquidation behaviour under the linear temporary impact. Through numerical simulation, we further explain the influence of the changed parameters ρ , a , b , x , and α on the investors’ liquidation strategy X t in twelve scenarios. Some interesting properties have been found.

The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Abdul-Majid Wazwaz
Keyword(s):  
Porous Medium ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variable Coefficients ◽  
Scientific Models ◽  
Nonlinear Ordinary Differential Equations ◽  
Nonlinear Odes ◽  
Variational Iteration ◽  
Hybrid Selection ◽  
Linear And Nonlinear

AbstractWe apply the variational iteration method (VIM) for solving linear and nonlinear ordinary differential equations with variable coefficients. We use distinct Lagrange multiplier for each order of ODE. We emphasize the power of the method by testing a variety of models with distinct orders and variable coefficients. Scientific models, namely, the hybrid selection model, the Thomas-Fermi equation, the Kidder equation of the Unsteady flow of gas through a porous medium, and the Riccati equation, are studied as well.

scholarly journals OPTIMAL LIQUIDATION UNDER STOCHASTIC PRICE IMPACT

2019 ◽  
Vol 22 (02) ◽  
pp. 1850059 ◽  
Author(s):  
WESTON BARGER ◽  
MATTHEW LORIG
Keyword(s):  
Continuous Time ◽  
Value Function ◽  
Price Impact ◽  
Trading Strategies ◽  
Impact Model ◽  
Optimal Liquidation ◽  
Special Cases ◽  
Time Price ◽  
Hamilton Jacobi Bellman ◽  
The Value Function

We assume a continuous-time price impact model similar to that of Almgren–Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop trading strategies for a trader who desires to liquidate his inventory but faces price impact as a result of his trading. For a fixed trading horizon, we perform coefficient expansion on the Hamilton–Jacobi–Bellman (HJB) equation associated with the trader’s value function. The coefficient expansion yields a sequence of partial differential equations that we solve to give closed-form approximations to the value function and optimal liquidation strategy. We examine some special cases of the optimal liquidation problem and give financial interpretations of the approximate liquidation strategies in these cases. Finally, we provide numerical examples to demonstrate the effectiveness of the approximations.

Study on The Self-Adaptive Forecast and Optimal Control Method for Grinding Wheel Infeed

2007 ◽  
Vol 329 ◽  
pp. 87-92
Author(s):  
Gui Jie Liu ◽  
Ning Mei ◽  
Ya Dong Gong ◽  
Wan Shan Wang
Keyword(s):  
Optimal Control ◽  
Computer Simulation ◽  
Control Method ◽  
The Self ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Optimal Control Method ◽  
Grinding System ◽  
Self Adaptive

A self-adaptive forecast & optimal control method for grinding wheel in-feed is presented, it can control grinding wheel plunge by using the new program of grinding process, and can compensate availably the size errors produced by the elasticity deflection of the grinding system and the deference of work-pieces rough and the wear of the grinding wheel, et al. The result of computer simulation and real testing indicate that this method can improve grinding quality.

An Optimal Control Approach to the Path Tracking Problem for an Automobile

1986 ◽  
Vol 10 (4) ◽  
pp. 233-241 ◽  
Author(s):  
H. Hatwal ◽  
E.C. Mikulcik
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Lane Change ◽  
Control Methods ◽  
Tracking Problem ◽  
Control Approach ◽  
Optimal Control Method ◽  
Linear And Nonlinear ◽  
Optimal Control Methods ◽  
Optimal Control Approach

The problem of determining the steering required for an automobile to follow a specified path is investigated using exact inverse and optimal control methods applied to simple linear and nonlinear vehicle models in lane-change maneuvers. The optimal control method results in solutions which provide for reasonably close tracking of the specified trajectories, but with reduced steering activity in comparison with what would be required for exact tracking, and also with less severe excursions in the slip angles, yaw rates and lateral accelerations. The results appear to be qualitatively consistent with the manner in which a real driver would react and the method could find applicability as a tool to compare the handling properties of different vehicles in a manner analogous to that of test drivers following a specified test course.

scholarly journals A Class of Optimal Liquidation Problem with a Nonlinear Temporary Market Impact

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jiangming Ma ◽  
Di Gao
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Strategy ◽  
Control Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Specific Form ◽  
The Self ◽  
Market Impact ◽  
Investment Environment ◽  
Optimal Control Method

We extend the self-exciting model by assuming that the temporary market impact is nonlinear and the coefficient of the temporary market impact is an exponential function. Through optimal control method, the optimal strategy satisfies the second-order nonlinear ordinary differential equation. The specific form of the optimal strategy is given, and the decreasing property of the optimal strategy is proved. A numerical example is given to illustrate the financial implications of the model parameter changes. We find that the optimal strategy of a risk-neutral investor changes with time and investment environment.

Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

2018 ◽  
pp. 66-78
Author(s):  
V. M. Artyushenko ◽  
V. I. Volovach
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Systems ◽  
Random Processes ◽  
Mathematical Transformation ◽  
Positive And Negative Feedback ◽  
Non Linear Systems ◽  
Linear And Nonlinear ◽  
Non Gaussian ◽  
Linear And Nonlinear Systems ◽  
Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

The human-like trajectory planning for autonomous vehicles based on optimal control in a test track environment

2021 ◽  
pp. 095440702110090
Author(s):  
Xing Xu ◽  
Minglei Li ◽  
Feng Wang ◽  
Ju Xie ◽  
Xiaohan Wu ◽  
...  
Keyword(s):  
Optimal Control ◽  
Autonomous Vehicles ◽  
Optimal Trajectory ◽  
Control Method ◽  
Autonomous Vehicle ◽  
Trajectory Data ◽  
Test Track ◽  
Optimal Control Method ◽  
The Future ◽  
On The Road

A human-like trajectory could give a safe and comfortable feeling for the occupants in an autonomous vehicle especially in corners. The research of this paper focuses on planning a human-like trajectory along a section road on a test track using optimal control method that could reflect natural driving behaviour considering the sense of natural and comfortable for the passengers, which could improve the acceptability of driverless vehicles in the future. A mass point vehicle dynamic model is modelled in the curvilinear coordinate system, then an optimal trajectory is generated by using an optimal control method. The optimal control problem is formulated and then solved by using the Matlab tool GPOPS-II. Trials are carried out on a test track, and the tested data are collected and processed, then the trajectory data in different corners are obtained. Different TLCs calculations are derived and applied to different track sections. After that, the human driver’s trajectories and the optimal line are compared to see the correlation using TLC methods. The results show that the optimal trajectory shows a similar trend with human’s trajectories to some extent when driving through a corner although it is not so perfectly aligned with the tested trajectories, which could conform with people’s driving intuition and improve the occupants’ comfort when driving in a corner. This could improve the acceptability of AVs in the automotive market in the future. The driver tends to move to the outside of the lane gradually after passing the apex when driving in corners on the road with hard-lines on both sides.

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