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On exact null controllability of Black-Scholes equation. (English) Zbl 1177.93021

Summary: 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.

MSC:

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
91G10 Portfolio theory
45K05 Integro-partial differential equations
93E03 Stochastic systems in control theory (general)
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
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References:

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