On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel, Krishnan Balachandran, Rangarajan Sowrirajan, Jeong Hoon Kim

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we discuss the exact null controllability of linear as well as nonlinear Black-Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with L2 topology.

Original languageEnglish
Pages (from-to)685-704
Number of pages20
JournalKybernetika
Volume44
Issue number5
Publication statusPublished - 2008 Dec 1

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Black-Scholes Equation
Null Controllability
Exact Controllability
Observability
Controllability
Topology
Observability Inequality
Carleman Estimate
Stock Prices
Dual Problem
Interest Rates
Volatility
Fixed point theorem
Nonlinear Equations
Influence

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Theoretical Computer Science
  • Software
  • Information Systems
  • Artificial Intelligence
  • Electrical and Electronic Engineering

Cite this

Sakthivel, K., Balachandran, K., Sowrirajan, R., & Kim, J. H. (2008). On exact null controllability of Black-Scholes equation. Kybernetika, 44(5), 685-704.
Sakthivel, Kumarasamy ; Balachandran, Krishnan ; Sowrirajan, Rangarajan ; Kim, Jeong Hoon. / On exact null controllability of Black-Scholes equation. In: Kybernetika. 2008 ; Vol. 44, No. 5. pp. 685-704.
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Sakthivel, K, Balachandran, K, Sowrirajan, R & Kim, JH 2008, 'On exact null controllability of Black-Scholes equation', Kybernetika, vol. 44, no. 5, pp. 685-704.

On exact null controllability of Black-Scholes equation. / Sakthivel, Kumarasamy; Balachandran, Krishnan; Sowrirajan, Rangarajan; Kim, Jeong Hoon.

In: Kybernetika, Vol. 44, No. 5, 01.12.2008, p. 685-704.

Research output: Contribution to journalArticle

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Sakthivel K, Balachandran K, Sowrirajan R, Kim JH. On exact null controllability of Black-Scholes equation. Kybernetika. 2008 Dec 1;44(5):685-704.