Generalized measure Black–Scholes equation: towards option self-similar pricing

IF 2 3区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Optimization and Engineering Pub Date : 2024-04-05 DOI:10.1007/s11081-024-09885-5

Nizar Riane, Claire David

引用次数: 0

Abstract

In this work, we give a generalized formulation of the Black–Scholes model. The novelty resides in considering the Black–Scholes model to be valid on ’average’, but such that the pointwise option price dynamics depends on a measure representing the investors’ ’uncertainty’. We make use of the theory of non-symmetric Dirichlet forms and the abstract theory of partial differential equations to establish well posedness of the problem. A detailed numerical analysis is given in the case of self-similar measures.

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广义计量布莱克-斯科尔斯方程：走向期权自相似定价

在这项工作中，我们给出了布莱克-斯科尔斯模型的广义表述。其新颖之处在于，我们认为布莱克-斯科尔斯模型 "平均 "有效，但点式期权价格动态取决于代表投资者 "不确定性 "的度量。我们利用非对称 Dirichlet 形式理论和偏微分方程抽象理论来确定问题的假设性。在自相似度量的情况下，我们给出了详细的数值分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Optimization and Engineering 工程技术-工程：综合

CiteScore

4.80

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Optimization and Engineering is a multidisciplinary journal; its primary goal is to promote the application of optimization methods in the general area of engineering sciences. We expect submissions to OPTE not only to make a significant optimization contribution but also to impact a specific engineering application. Topics of Interest: -Optimization: All methods and algorithms of mathematical optimization, including blackbox and derivative-free optimization, continuous optimization, discrete optimization, global optimization, linear and conic optimization, multiobjective optimization, PDE-constrained optimization & control, and stochastic optimization. Numerical and implementation issues, optimization software, benchmarking, and case studies. -Engineering Sciences: Aerospace engineering, biomedical engineering, chemical & process engineering, civil, environmental, & architectural engineering, electrical engineering, financial engineering, geosciences, healthcare engineering, industrial & systems engineering, mechanical engineering & MDO, and robotics.