On exact null controllability of Black-Scholes equation

Kumarasamy Sakthivel; Krishnan Balachandran; Rangarajan Sowrirajan; Jeong-Hoon Kim

Kybernetika (2008)

  • Volume: 44, Issue: 5, page 685-704
  • ISSN: 0023-5954

Abstract

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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 L 2 topology.

How to cite

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Sakthivel, Kumarasamy, et al. "On exact null controllability of Black-Scholes equation." Kybernetika 44.5 (2008): 685-704. <http://eudml.org/doc/33957>.

@article{Sakthivel2008,
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 $L^2$ topology.},
author = {Sakthivel, Kumarasamy, Balachandran, Krishnan, Sowrirajan, Rangarajan, Kim, Jeong-Hoon},
journal = {Kybernetika},
keywords = {Black–Scholes equation; volatility; controllability; observability; Carleman estimates; Black-Scholes equation; volatility; controllability; observability; Carleman estimates},
language = {eng},
number = {5},
pages = {685-704},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On exact null controllability of Black-Scholes equation},
url = {http://eudml.org/doc/33957},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Sakthivel, Kumarasamy
AU - Balachandran, Krishnan
AU - Sowrirajan, Rangarajan
AU - Kim, Jeong-Hoon
TI - On exact null controllability of Black-Scholes equation
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 5
SP - 685
EP - 704
AB - 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 $L^2$ topology.
LA - eng
KW - Black–Scholes equation; volatility; controllability; observability; Carleman estimates; Black-Scholes equation; volatility; controllability; observability; Carleman estimates
UR - http://eudml.org/doc/33957
ER -

References

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