Spectrally negative Lévy processes
Scale functions, fluctuation identities, first-passage problems, path decompositions, and Doob h-transforms.
Associate Professor · Middle East Technical University
Ceren Vardar Acar
Probability Theory · Lévy Processes · Fractional Brownian Motion
I am an Associate Professor in the Department of Statistics at Middle East Technical University (METU). My research focuses on stochastic processes and their path properties, with particular emphasis on spectrally negative Lévy processes, fractional Brownian motion, extreme values, maximum drawdown and drawup, fluctuation theory, and applications in risk and financial mathematics.
METUDepartment of Statistics
ProbabilityStochastic processes & path properties
RiskExtreme values · drawdown · drawup
Financial MathLévy and Markov additive models
Research
Research highlights
I study probabilistic structures that connect path behavior, extremes, and quantitative risk.
Maximum drawdown & drawup
Joint and conditional laws of maximum losses and gains, ordering of terminal extrema, and Brownian specializations.
Extreme values & risk
Stochastic-process path properties, risk analysis, financial mathematics, and applications involving rare or extreme events.
Fractional Brownian motion
Suprema and maximum-loss functionals, drifted models, Hurst-parameter estimation, discretization and random-walk approximations, with applications to commodity-price cycles.
Fractional Brownian Motion
A continuing research strand
My work on fractional Brownian motion studies extremes and path-dependent loss measures, statistical estimation of long-range dependence, approximation methods, and applications to financial and commodity-price data.
- 2011 — Results on the supremum of fractional Brownian motion.
- 2013 — Distribution of maximum loss of fractional Brownian motion with drift.
- 2014 — Estimation of the Hurst parameter using the CMARS method.
- 2015 — Bounds on the expected value of maximum loss of fractional Brownian motion.
- 2020 — Discretization and correlated random-walk approximations to fractional Brownian motion.
- 2026 — Maximum-drawdown analysis of crude-oil super cycles using fractional Brownian motion.
“The same curiosity that drives a proof can also question the way we look at the world and this inhumane system surrounding us. ”
Grants
Selected grants & funded projects
Research support for work on Lévy processes, fractional Brownian motion, extremes, drawdown duration, and quantitative risk.
Joint Distributions of Maximum Drawup/Drawdown Values and Their Durations in Lévy Processes, with Applications to Asset and Insurance Pricing
Principal Investigator · Project No. 124F094 · with Mine Çağlar and İ. Ünalmış.
Project record ↗Distribution and Expected Value of Maximum Drawdown Duration in Asset Prices under Lévy and Diffusion Models
Principal Investigator · International bilateral collaboration with Florin Avram.
Path Properties of Lévy Processes and Joint Distributions of Maximum Loss and Maximum Gain
Principal Investigator · Higher Education Institutions supported project · with Mine Çağlar.
Distributional Properties of Maximum Loss in Fractional Brownian Motion and Lévy Processes
Principal Investigator · Early-career research project on path extrema and maximum-loss distributions.
Publications
Selected publications & current work
2026
Joint Laws of Maximum Drawdown and Maximum Drawup for Spectrally Negative Lévy Processes
With Emre Akdoğan · arXiv:2609.03634. Current work on conditional path decompositions, scale functions, and ordered extrema. arXiv ↗
2026
Conditional Path Decomposition at the Infimum and Maximum Drawdowns for Spectrally Negative Lévy Processes
With Mine Çağlar · arXiv:2606.27573. arXiv ↗
2026
Stopping Levels for a Spectrally Negative Markov Additive Process
Communications in Mathematics and Statistics, 14(2), 369–390.
2026
Has the Last Super Cycle in Crude Oil Price Ended? A Maximum Drawdown Approach using Fractional Brownian Motion
Applied Stochastic Models in Business and Industry, 42.
2022
An Optimal Stopping Problem for Spectrally Negative Markov Additive Processes
Stochastic Processes and their Applications, 150, 1109–1138.
2021
Maximum Drawdown and Drawdown Duration of Spectrally Negative Lévy Processes Decomposed at Extremes
Journal of Theoretical Probability, 34(3), 1486–1505.
2020
The W, Z Scale Functions Kit for First Passage Problems of Spectrally Negative Lévy Processes, and Applications to Control Problems
ESAIM: Probability and Statistics, 24, 454–525.
2017
Maximum Loss and Maximum Gain of Spectrally Negative Lévy Processes
Extremes, 20(2), 301–308.
Talks & Conferences
Recent and invited presentations
Selected international meetings and presentations.
9–11 Sep 2026
EAJ 2026 · Istanbul
Correlation of Maximum Drawdown and Maximum Drawup for Spectrally Negative Lévy Processes
7th European Actuarial Journal Conference, Istanbul, Türkiye. Joint work with Emre Akdoğan.
8–10 Aug 2026
EcoSta 2026 · Kyoto
Joint distributions of maximum drawdown and maximum drawup for spectrally negative Lévy processes
9th International Conference on Econometrics and Statistics, Ryukoku University, Kyoto, Japan.
22–25 Apr 2024
Invited Talk · Isaac Newton Institute
Exit Times and Extremes of Fractional Brownian Motion and Spectrally Negative Lévy Processes
Workshop “SGD: Stability, Momentum Acceleration and Heavy Tails”, Isaac Newton Institute for Mathematical Sciences; workshop held at The Alan Turing Institute, London.
Talk page / recording ↗Organized Workshops and Conferences
16–17 October 2026
6th Ankara-Istanbul Workshop on Stochastic Processes
16–17 June 2016
3rd Ankara-Istanbul Workshop on Stochastic Processes
17-20 May 2012
International Conference on Applied Mathematics & Approximation Theory
Teaching
Teaching & supervision
Probability, inference, and stochastic-process courses from foundational to graduate level.
Advanced Probability Theory
Sigma Algebras, Random Variables, Weak Law of Large Numbers, Strong Law of Large Numbers, Independence of Sigma Algebras, Central Limit Theorems.
Advanced Statistical Inference
Likelihood methods, testing, estimation, and advanced inferential reasoning.
Stochastic Differential Equations
Ito Calculus.
Stochastic Processes in Machine Learning
Bayesian inference, MCMC, Sequential Monte Carlo and Hidden Markov Models.
Multivariate Analysis
Multivariate normal theory, MANOVA, principal components, factor analysis, classification, clustering, and canonical correlation.
Introduction to Financial Engineering
Stochastic modeling, Black-Scholes Model, risk, extremes, and applications of probability in finance and insurance.
Stochastic Processes
Markov chains, Poisson processes, renewal ideas, and stochastic-process foundations.
Probability Theory
Random variables, distributions, expectation, convergence, and probabilistic modeling.
CV
Academic background
Academic appointment
2020–present
Associate Professor, Department of Statistics, Middle East Technical University.
Education
PhD — Mathematics and Statistics, Bowling Green State University, 2008.
MSc — Statistics, Middle East Technical University, 2002.
BSc — Statistics, Middle East Technical University, 1999.
Research areas
Probability theory · stochastic processes · Lévy processes · fractional Brownian motion · path properties · extreme values · risk analysis · financial mathematics · asymptotic distributions.
Theses Graduate supervision
Research supervision in stochastic processes, Lévy processes, financial mathematics, extreme values, and related applications.
PhD — JOINT DISTRIBUTIONS OF THE MAXIMUM DRAWDOWN ANDMAXIMUM DRAWUP IN LÉVY PROCESSES, Vardar Acar C. (Supervisor), E.AKDOĞAN, PhD, 2025.
MSc — QUANTUM RANDOM WALK SIMULATION USING DEPENDENT RANDOM WALK Vardar Acar C. (Supervısor), M.KAŞİF, MSc, 2024.
MSc — Methodology of identifying super-cycles in silver prices, Vardar Acar C. (Supervısor), T.SOYSAL, Msc, 2023.
MSc — Various parameter estimation techniques for stochastic differential equations, Vardar Acar C. (Supervısor), S.ERGİŞİ, Msc, 2019.
MSc — Parameter estimation in merton jump diffusion model, Vardar Acar C. (Supervisor), T.ADEM, Msc, 2019.
MSc — A generalized correlated random walk approximation to fractional brownian motion, Vardar Acar C. (Supervisor), B.COŞKUN, Msc, 2018.
MSc — Duration of maximum drawdown in oil prices, Vardar Acar C. (Supervisor), M.SALCI, Msc, 2018.
MSc — Stochastic delay differential equations, Vardar Acar C. (Co-Supervisor), E.EZGİ, MSc, 2017.
MSc — Hisse senetlerinde olabilecek en büyük kaybın asimptotik dağılımı uygulamaları, VARDAR ACAR C. (Supervisor), Z.İSLAMOV, MSc, 2013.
MSc — Kesikli stokastik popülasyon modelleri ve gecikme etkisi, VARDAR ACAR C. (Supervisor), E.EMİN, Msc, 2013.
MSc — Kesirli brown hareketinin maksimum kayıp ve supremum değişkenleri, VARDAR ACAR C. (Supervisor), H.ÇAKAR, MSc, 2012.
Doctorate Dissertation Award
The Best Thesis in Doctorate in Financial Mathematics Program for the year 2024-2025 Thesis Advisor Ceren Vardar Acar of Emre Akdoğan Graduate School of Applied Mathematics, METU.
Beyond Research
Life beyond equations
Family, travel, nature, and the moments in between.
Contact
Get in touch
I am happy to hear from colleagues, students, and potential collaborators.