Invariance of convex sets: An alternative proof and application to Black-Scholes operator

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Chakir Hilmi
Ahmed Sani
Samir Elmourchid

Abstract

An alternative proof of invariance of convex sets by the solution of non autonomous Cauchy problem is given. The proof is based on the recent integral approximation of time dependent operators A(t) acting on Hilbert space when they are associated with smooth sesquilinear forms a(t,.,.) defined on common dense domain and the known Chernoff Product Formula. An application to positivity of Black-Scholes operator is given.

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How to Cite
Hilmi, C., Sani, A., & Elmourchid, S. (2022). Invariance of convex sets: An alternative proof and application to Black-Scholes operator. Gulf Journal of Mathematics, 13(1), 101-109. Retrieved from https://gjom.org/index.php/gjom/article/view/929
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