凸集的不变性:Black-Scholes算子的另一种证明及其应用

Gulf Journal of Mathematics Pub Date : 2022-07-19 DOI:10.56947/gjom.v13i1.929

Chakir Hilmi, A. Sani, Samir Elmourchid

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引用次数: 0

摘要

给出了用非自治柯西问题的解证明凸集不变性的另一种方法。本文的证明是基于Hilbert空间上的时间相关算子A(t)与定义在公共稠密域上的光滑半线性形式A(t，.，.)以及已知的Chernoff积公式相关联时的积分近似。给出了Black-Scholes算子正性的一个应用。

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

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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Gulf Journal of Mathematics

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