NİCEL KARAR MODELLERİ İÇİN LÉVY SÜREÇLERİNE GİRİŞ: KURAMSAL ÇERÇEVE

Akbar  BARATI CHIYANEH; Hamit  MİRTAGİOĞLU; Yıldırım  DEMİR

doi:10.63127/tuaz.by.220

INTRODUCTION TO LÉVY PROCESSES FOR QUANTITATIVE DECISION MODELS: THEORETICAL FRAMEWORK

Authors

Assist. Prof. Akbar Baratı Chıyaneh

University of Tabriz

https://orcid.org/0000-0003-4401-5477

Prof. Hamit Mirtagioğlu

Bitlis Eren University

https://orcid.org/0000-0003-2952-9584

Assoc. Prof. Yıldırım Demir

Van Yüzüncü Yıl University

https://orcid.org/0000-0002-6350-8122

DOI: https://doi.org/10.63127/tuaz.by.220.c163

Synopsis

Introduction to Lévy Processes for Quantitative Decision Models: Theoretical Framework Accurate modeling of uncertainty in quantitative decision-making models is critical for the analysis of economic and financial systems. Brownian motion, frequently used in traditional models, falls short in explaining complex phenomena observed in financial markets such as sudden price jumps, volatility clustering, and heavy-tailed distributions. This study aims to present the theoretical framework of Lévy processes, which integrate drift, diffusion, and jump components within a unified structure. The study examines the historical development of stochastic processes, Lévy-Itô decomposition, the Lévy-Khinchine formula, and the mathematical properties of these processes in detail. This theoretical infrastructure, presented as an alternative to the limitations of deterministic approaches, constitutes the foundation for models to be developed in areas such as modern finance, risk analysis, and derivative pricing.

Author Biographies

Assist. Prof. Akbar Baratı Chıyaneh, University of Tabriz

Baratı Chıyaneh, Akbar
Assist. Prof. Akbar Baratı Chıyaneh serves as a faculty member at the Department of Applied Mathematics, Faculty of Mathematical, Statistical and Computer Sciences, University of Tabriz, Tabriz, Iran. Baratı Chıyaneh completed undergraduate education at Payame Noor University in the department of Mathematics in 2002, master's education at Tabriz Payame Noor University; Bitlis Eren University in the department of Optimization; Applied Statistics in 2006; 2024, and Ph.D. degree from Van Yüzüncü Yıl University in the field of Applied Mathematics in 2017. Primary research interests include numerical analysis, perturbation methods, stochastic differential equations, artificial neural networks and machine learning, optimization. Baratı Chıyaneh has national and international articles published.
E-mail: baratiakbar@tabrizu.ac.ir, baratiakbar@yahoo.com | ORCID: https://orcid.org/0000-0003-4401-5477

Prof. Hamit Mirtagioğlu, Bitlis Eren University

Mirtagioğlu, Hamit
Prof. Hamit Mirtagioğlu serves as a head of statistics department, head of applied statistics department at the Department of Statistics, Faculty of Arts and Sciences, Bitlis Eren University, Bitlis, Türkiye. Mirtagioğlu completed undergraduate education at Gazi University in the department of Statistics in 1987, and Ph.D. degree from Ankara University in the field of Animal Science Dept., Biometry and Genetics in 2001. Primary research interests include applied statistics. Mirtagioğlu has national and international articles and book chapters published in Turkish and English.
E-mail: hmirtagioglu@beu.edu.tr, hamitsa86@gmail.com | ORCID: https://orcid.org/0000-0003-2952-9584

Assoc. Prof. Yıldırım Demir, Van Yüzüncü Yıl University

Demir, Yıldırım
Assoc. Prof. Yıldırım Demir serves as a faculty member at the Department of Econometrics, Faculty of Economics and Administrative Sciences, Van Yüzüncü Yıl University, Van, Türkiye. Demir completed undergraduate education at Marmara University in the department of Electrical Education in 2001, master's education at Van Yüzüncü Yıl University in the department of Animal Science Dept., Biometry and Genetics in 2008, and Ph.D. degree from AtaTürk University in the field of Animal Science Dept., Biometry and Genetics in 2016. Primary research interests include applied statistics, quantitative decision methods. Demir has national and international articles and book chapters published in Turkish and English.
E-mail: ydemir@yyu.edu.tr, ydemir.yyu@gmail.com | ORCID: https://orcid.org/0000-0002-6350-8122