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

Tiwari Archana, Bhattacharyya Debanjana, Pati K. C.

Archives of Control Sciences

2020

Vol. 30, No. 3

553--573

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-Scholes equation can be mapped to one dimensional free Schrödinger equation. 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.

Ulam-Hyers stability of a parabolic partial differential equation

Marian Daniela, Ciplea Sorina Anamaria, Lungu Nicolaie

Demonstratio Mathematica

2019

Vol. 52, nr 1

475--481

The goal of this paper is to give an Ulam-Hyers stability result for a parabolic partial differential equation. Here we present two types of Ulam stability: Ulam-Hyers stability and generalized Ulam-Hyers-Rassias stability. Some examples are given, one of them being the Black-Scholes equation.