Controllability and hedgibility of black-scholes equations with n stocks

K. Sakthivel; J. H. Kim

doi:10.1007/s10440-009-9548-8

Controllability and hedgibility of black-scholes equations with n stocks

K. Sakthivel, J. H. Kim

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is to investigate the controllability and observability properties of linear and certain nonlinear Black-Scholes (B-S) type equations consisting of N stocks in an appropriate bounded domain I of ℝ ₊ ^N . In this model both the stock volatility and interest rate are influenced by the stock prices and the control which is related to the hedging ratio in option pricing of finance is distributed over a subdomain of I. The proof of the controllability result for the linear B-S equations relies on the suitable observability inequality for the associated adjoint problem, and for the nonlinear model, fixed point technique is applied. Our result leads to that the dynamic hedgibility in finance is proved in the context of controllability theory.

Original language	English
Pages (from-to)	339-363
Number of pages	25
Journal	Acta Applicandae Mathematicae
Volume	111
Issue number	3
DOIs	https://doi.org/10.1007/s10440-009-9548-8
Publication status	Published - 2010 Sept

Bibliographical note

Funding Information:
Acknowledgements The first author work was supported by the Brain Korea 21 project at Yonsei University, 2008 and the second author work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2008-314-C00045) and in part by the MKE and KIAT through the Workforce Development Program in Strategic Technology.

All Science Journal Classification (ASJC) codes

Applied Mathematics

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10.1007/s10440-009-9548-8

Cite this

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abstract = "This paper is to investigate the controllability and observability properties of linear and certain nonlinear Black-Scholes (B-S) type equations consisting of N stocks in an appropriate bounded domain I of ℝ + N . In this model both the stock volatility and interest rate are influenced by the stock prices and the control which is related to the hedging ratio in option pricing of finance is distributed over a subdomain of I. The proof of the controllability result for the linear B-S equations relies on the suitable observability inequality for the associated adjoint problem, and for the nonlinear model, fixed point technique is applied. Our result leads to that the dynamic hedgibility in finance is proved in the context of controllability theory.",

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N2 - This paper is to investigate the controllability and observability properties of linear and certain nonlinear Black-Scholes (B-S) type equations consisting of N stocks in an appropriate bounded domain I of ℝ + N . In this model both the stock volatility and interest rate are influenced by the stock prices and the control which is related to the hedging ratio in option pricing of finance is distributed over a subdomain of I. The proof of the controllability result for the linear B-S equations relies on the suitable observability inequality for the associated adjoint problem, and for the nonlinear model, fixed point technique is applied. Our result leads to that the dynamic hedgibility in finance is proved in the context of controllability theory.

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Controllability and hedgibility of black-scholes equations with n stocks

Abstract

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