Black-Scholes Model and Martingale functions of a Brownian Motion

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B. Chikvinidze
Georgian-American University; Institute of Cybernetics of Georgian Technical University
M. Mania
Georgian-American University; Razmadze Mathematical Institute of Tbilisi State University
R. Tevzadze
Georgian-American University; Institute of Cybernetics of Georgian Technical University

Abstract

Using a description of time-dependent martingale functions of a Brownian Motion and some natural assumptions (axioms), we show that the evolution of the asset price process should follow to the geometric Brownian Motion.

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Keywords:
Brownian Motion, Martingales, Functional Equations, Black- Scholes model
Published: Dec 23, 2024
DOI: https://doi.org/10.62232/barp.9.2024.8571

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How to Cite
Chikvinidze, B., Mania, M., & Tevzadze, R. (2024). Black-Scholes Model and Martingale functions of a Brownian Motion. Business Administration Research Papers, 9. https://doi.org/10.62232/barp.9.2024.8571
Issue
Vol. 9 (2024): Applications of Stochastic Processes and Mathematical Statistics to Financial Economics and Social Sciences IX
Section
Conference Materials
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