Controllability and hedgibility of black-scholes equations with n stocks

K. Sakthivel, J. H. Kim

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)339-363
Number of pages25
JournalActa Applicandae Mathematicae
Volume111
Issue number3
DOIs
Publication statusPublished - 2010 Sep

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Black-Scholes Equation
Controllability
Observability
Finance
Observability Inequality
Adjoint Problem
Black-Scholes
Hedging
Stock Prices
Option Pricing
Interest Rates
Volatility
Nonlinear Model
Bounded Domain
Linear equation
Fixed point
Costs
Model

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

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Controllability and hedgibility of black-scholes equations with n stocks. / Sakthivel, K.; Kim, J. H.

In: Acta Applicandae Mathematicae, Vol. 111, No. 3, 09.2010, p. 339-363.

Research output: Contribution to journalArticle

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