Black-Scholes方程相关群的可控性和稳定性分析

IF 1.1 4区计算机科学 Q4 AUTOMATION & CONTROL SYSTEMS

Archives of Control Sciences Pub Date : 2023-07-20 DOI:10.24425/acs.2020.134677

Archana Tiwari, Debanjana Bhattacharyya

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引用次数: 0

摘要

本文用保角变换研究了由Black-Scholes方程不变性引起的李群上的无漂移控制系统。这些类型的研究是可能的，因为布莱克-斯科尔斯方程可以映射到一维自由Schrödingerequation。特别地，我们研究了系统的可控性、最优控制以及稳定性。我们还通过两个非常规积分器和常规龙格-库塔积分器找到了系统的状态轨迹。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Controllabilty and stability analysis on a group associated with Black-Scholes equation

In this paper we have studied the driftless control system on a Lie group which arises due to the invariance of Black-Scholes equation by conformal transformations. These type of studies are possible as Black-Scholesequation can be mapped to one dimensional free Schrödingerequation. In particular we have studied the controllability, optimal control of the resulting dynamics as well as stability aspects of this system. We have also found out the trajectories of the states of the system through two unconventional integrators along with conventional Runge-Kutta integrator.

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来源期刊

Archives of Control Sciences Mathematics-Modeling and Simulation

CiteScore

2.40

自引率

33.30%

发文量

审稿时长

14 weeks

期刊介绍： Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.