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Welcome to the homepage of Prof. Dr. Alfred Müller

Alfred Müller is a member of the Stochastics working group.

Stochastics working group
Foto von Alfred Müller

Courses

Summer semester 2026
Title of the course Moodle Unisono
Stochastic Dynamic Optimization VL Ü
Title of the course Moodle unisono
Stochastics III(formerly Financial Engineering) Course VL Ü
Advanced Mathematics for Business and Economics Course VL Ü

Contact us

  • mueller@mathematik.uni-siegen.de
  • +49 271 740-3587 (phone)
  • +49 271 740-3627 (Fax)
Please arrange a personal appointment by e-mail.
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Academic career

  • Diploma studies in mathematics

    University of Karlsruhe (1986 - 1991)
    Diploma thesis: Bayesian models for sequential sales problems
    Supervisor: Karl Hinderer

  • Doctorate

    University of Karlsruhe (February 1995)
    Dissertation: Integral induced orders and metrics on sets of probability measures with applications to Markoff decision processes
    Supervisor: Karl Hinderer

  • Habilitation

    University of Karlsruhe (January 2000)
    Habilitation thesis: Stochastic Orders and the Comparison of Size, Variability and Dependency of Risks

  • student assistant

    University of Karlsruhe (October 1988 - September 1991)

  • Research assistant

    University of Karlsruhe (October 1991 - September 1995)

  • Research Assistant (C1)

    University of Karlsruhe (October 1995 - September 2000)

  • Lecturer (C2)

    University of Karlsruhe (October 2000 - September 2006)

  • Substitute Professor

    University of Siegen (October 2006 - March 2007)

  • Senior Lecturer

    Heriot-Watt University, Edinburgh (April 2007 - March 2008)

  • Professor

    University of Siegen (since April 2008)

Alfred Müller is/was co-editor of the following journals:

Advances in Applied Probability
(2008 - 2025)
Journal of Applied Probability
(2008 - 2025)
Insurance: Mathematics and Economics
(since 2019)

  • Deputy Head of the Department of Mathematics

    University of Siegen, 2010 - 2012

  • Spokesperson of the Department of Mathematics

    University of Siegen, 2012 - 2014

  • Member of the doctoral committee Dr. rer. nat.

    University of Siegen, since 2018

  • Board member of the German Society for Actuarial and Financial Mathematics, since 2015
  • Chairman of the prize committee for the GAUSS Prize, since 2015

Research interests

  • Stochastic order relations and modeling of dependencies
  • Copula theory and Lévy-Copulas
  • Insurance and financial mathematics
  • Stochastic models for electricity markets and electricity derivatives
  • Risk measures
  • Markovian decision processes
  • Optimal stopping problems
  • Decision under risk and uncertainty

Publications

To the profile at Google Scholar

Monograph:

Comparison Methods for Stochastic Models and Risks

The monograph, written in collaboration with Dietrich Stoyan, was published by Wiley in 2002. It contains the latest research results (at the time of publication) in the field of stochastic order relations and various applications.

To the book

Cover des Buchs von Müller und Stoyan aus dem Jahr 2002

Publications at ORCID

To the profile at ORCID
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Journal article
2025

Some remarks on the effect of risk sharing and diversification for infinite mean risks

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2023

A copula-based time series model for global horizontal irradiation

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2023

Lp-norm spherical copulas

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2023

Multivariate Almost Stochastic Dominance: Transfer Characterizations and Sufficient Conditions Under Dependence Uncertainty

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2022

Technical Note—Ranking Distributions When Only Means and Variances Are Known

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2020

Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2018

Probabilistic forecasting of industrial electricity load with regime switching behavior

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Book chapter
2018

On Consistency of the Omega Ratio with Stochastic Dominance Rules

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2018

Expectiles, Omega Ratios and Stochastic Ordering

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2017

Between First- and Second-Order Stochastic Dominance

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2016

A multivariate design framework for river confluences

Authors: Univ.-Prof. Dr. Alfred Müller et al.
Journal article
2015

Detecting anthropogenic footprints in sea level rise

Authors: Univ.-Prof. Dr. Alfred Müller et al.

Lectures

  • Matthias Scherer (Technical University of Munich).
    Emil J. Gumbel (1891 - 1966): Mathematician - Publicist - Pacifist.
    50 years of the University of Siegen: Day of Mathematics and Physics - Scientific Lectures and Laboratory Tours, May 12, 2022.
  • Marco Oesting (University of Stuttgart).
    Of floods and storms of the century: Statistical modeling of extreme weather and climate events.
    50 years of the University of Siegen: Day of Mathematics and Physics - Scientific Lectures and Laboratory Tours, May 12, 2022.
  • Katharina Hees (Paul-Ehrlich-Institut).
    As a mathematician at the Paul-Ehrlich-Institut - The complex path to the approval of a vaccine.
    50 years of the University of Siegen: Days of Mathematics - Pandemic Focus Day, May 11, 2022.
  • Silvana Pesenti (University of Toronto).
    Robust Distortion Risk Measures.
    March 4, 2020.
  • Dirk Tasche (Swiss Financial Market Supervisory Authority (FINMA)).
    A case study on model risk in credit default estimates.
    Ceremonial event as part of the awarding of an honorary professorship to Dr. Carsten S. Wehn, January 31, 2020.
  • Bernhard Klar (Karlsruhe Institute of Technology).
    Old and new about the skewness of a distribution,
    July 2019.
  • Tom Fischer (University of Würzburg).
    Valuationin Financial Networks: Credit Default Swaps, Puts, Debt, and Equity,
    July 2019.
  • Florian Ziel (University of Duisburg-Essen).
    Marginal-Copula-Scores for Multivariate Forecasting Evaluation.
    Stochastic Colloquium, June 21, 2018.
  • Axel Bücher (Ruhr-Universität Bochum).
    On a Sliding Blocks Estimator for the Extremal Index.
    Workshop on Extreme Values in Meteorology and Hydrology, March 15, 2018.
  • Roland Fried (Technical University of Dortmund).
    Methods for Joint Estimation of Common Extreme Value Characteristics, With Applications to Regional Flood Frequency.
    Workshop on Extreme Values in Meteorology and Hydrology, March 15, 2018.
  • Martin Schlather (University of Mannheim).
    Geostatistical Modeling with Random Fields.
    Oberseminar Stochastik, June 13, 2017.
  • Cord Harms (University of Duisburg-Essen).
    Application of Structural Electricity Models for Dynamic Hedging.
    May 2017.
  • Julia Eisenberg (Vienna University of Technology).
    The Challenge of a Negative Interest Rate in Non-Life Insurance.
    Oberseminar Stochastik, May 27, 2016.
  • Carole Bernard (University of Waterloo).
    Risk Equity and Catastrophe Aversion Under Dependent Risks.
    Mathematical Colloquium, November 6, 2014.
  • Thijs Benschop (Humboldt-Universität zu Berlin).
    Volatility Modeling of CO2 Emission Allowance Spot Prices With Regime-Switching GARCH Models.
    Mathematical Colloquium, August 28, 2014.
  • Franziska Schulz (Humboldt-Universität zu Berlin).
    Forecasting Generalized Quantiles of Electricity Demand: A Functional Data Approach.
    Mathematisches Kolloquium, 28 August 2014.
  • Stefan Napel (University of Bayreuth).
    On the Democratic Weights of Nations.
    Mathematisches Kolloquium, July 10, 2014.
  • Corina Constantinescu (University of Liverpool).
    Ruin Probabilities in Risk Models With Gamma Distributed Claims.
    April 2014.

Selected research projects

The project Employee-centered qualification and digital assistance to increase energy and resource efficiency in SMEs (sustainKMU)
proactively supported employees of small and medium-sized enterprises (SMEs) in the independent and systematic implementation of IT-supported energy and resource optimization strategies.

As part of the research project User-oriented Smart Environmental Information Systems in Practice (ASUP)
the aim was to develop user-oriented and smart environmental information systems that allow companies to easily and effectively identify and subsequently quantify electricity-based savings potential and measures.

The third-party funded project Living Lab - Energy and Environment, financed by the Ministry for Climate Protection, Environment, Agriculture, Nature Conservation and Consumer Protection of the State of North Rhine-Westphalia, was dedicated to the topics of energy transition, energy management, energy controlling and energy efficiency in companies. As part of the energy analysis and mathematical models work package, Alfred Müller's chair dealt with the modeling and estimation of risks in energy markets.

The project, which was financed by EnBW, examined stochastic models for the prices of electricity, gas and other commodities and the consequences for the prices of supply contracts and spread options.

Supervised theses

  1. Florian Bäcker (2010) - The Propp-Wilson algorithm for the simulation of stationary distributions of Markov chains
  2. Friederike Runge (2010) - Solution concepts for cooperative games
  3. Sebastian Schirdewahn (2010) - Generalized linear models and IBNR techniques
  4. Sebastian Kühnert (2010) - Distribution invariant risk measures and shortfall risk
  5. Johan Ulrich Mouissi (2010) - Models for Credit Spreads
  6. Heike Riensberg (2010) - Valuation of credit derivatives
  7. Julia Müller (2011) - Lundberg bounds for risk processes and subexponentially distributed losses
  8. Natalie Schmücker (2011) - Dynamic risk measures
  9. Peter Siembab (2011) - Modeling of credit risks
  10. Sarah Schneider (2011) - Valuation of credit default swaps and first-to-default swaps
  11. Olga Kaiter (2011) - Dependency concepts and the comparison of dependencies in actuarial mathematics
  12. Tatiana Pantack (2011) - Methods for the construction of copulas
  13. Katharina Schneider (2011) - Operational risks with subexponential distributions
  14. Kevin Berk (2012) - Time series analysis for electricity prices
  15. Lars Blume (2012) - Time series models of the type ARMA and GARCH
  16. Carola Bilgen (2012) - Mixed Poisson processes
  17. Philipp Dirschke (2012) - Probabilities of ruin in risk processes
  18. Daniel Schulte (2013) - Valuation of an endless American put option in a binomial model
  19. Matthias Reuber (2014) - On the number and probability of Champions League round of 16 match schedules
  20. Cyrille Pongui (2014) - Dynamic credit risk models and credit derivatives
  21. Nicolas Nbakwala (2014) - Systemic risk measures
  22. Sascha Reeh (2015) - Heavy tailed distributions and their detection
  23. Ines Münker (2015) - Marshall-Olkin Copulas
  24. Lars Mattejiet (2015) - Fundamental theorem of option pricing
  25. Thomas Mörsdorf (2016) - Optimal portfolios with utility maximization in the one-period model
  26. Maximilian Stock (2016) - The application of Markovian decision processes to optimization problems in financial mathematics
  27. Matthias Klemm (2016) - Detection of photovoltaic production in electricity load profiles using linear regression
  28. Christopher Hohe (2016) - Expectiles as risk measures
  29. Waldemar Ulrich (2017) - Dependency measures for copulas
  30. Shuai Wang (2017) - Renewal processes
  31. Marius Hermes (2017) - The rearranement algorithm
  32. Alexandra Schmidt (2018) - Bayesian models and credibility theory
  33. Katharina Stracke (2019) - The Omega Ratio performance measure and its consistency with respect to stochastic dominance
  34. Robin Mey (2020) - Markov chains, Lyapunov functions and martingales
  35. Paul Hesse (2023) - A concept for approximate stochastic dominance
  36. Lucas Fischbach (2023) - Copula-based credit risk models
  37. Amelie Melcher (2025). Marshall-Olkin Copulas.
  38. Leonie Westmeier (2025). Multivariate normal distributions and elliptical distributions.

  39. Juliana Leidig (2025). Dependency measures for random variables: Kendall's tau and Spearman's rho.

     

  1. Jan Müller (2010) - A coupled spot market model for oil and gas prices
  2. Dennis Ziegner (2010) - Medical inflation: determination and forecasting
  3. Tatiana Wandraj (2011) - Stochastic modeling and simulation of the capital market for the evaluation of investment strategies
  4. Alexander Müller (2011) - Monte Carlo methods for the valuation of swing options
  5. Michael Alterauge (2011) - A model for the valuation of special energy supply contracts
  6. Natalie Schmücker (2013) - Variance-reducing methods in market risk
  7. Sebastian Schirdewahn (2013) - Statistical analysis of data relevant for supply capability and optimization of supply capability
  8. Julia Müller (2013) - Expectile as a risk measure in the special case of shortfall risk
  9. Kevin Berk (2013) - Modeling and Forecasting Medium-Term Electricity Demand of Enterprises From Various Business Sectors
  10. Jean Zimmermann (2014) - Stochastic Modeling of Spot Prices on the Spanish Electricity Market
  11. Katrin Fiala (2015) - Hierarchical Archimedean Copulas
  12. Matthias Reuber (2015) - Stochastic models for the yield of photovoltaic systems
  13. Christine Braun (2015) - Sensitivity analysis for options on energy markets based on the Least Squares Monte Carlo method
  14. Olivia Luczynski (2016) - Unsteady bivariate time series for flood data
  15. Anke Kramer (2017) - Sparse Models for Short-Term Forecasting of Electricity Load
  16. Matthias Klemm (2018) - Stochastic models for electricity prices in intraday exchange trading
  17. Christopher Hohe (2018) - Statistical analysis of cryptocurrencies
  18. Sarah-Fee Schuhen (2018) - Quantification of Wrong Way Risk in the XVA Calculation
  19. Annika Dietrich (2018) - Spatial extremal dependencies of wind data
  20. Lars Mattejiet (2020) - Expected loss burden of silent cyber in commercial property insurance from a reinsurance perspective based on exposure curves
  21. Katharina Stracke (2020) - Regression models for photovoltaic and radiation data
  22. Julian Kappel (2020) - Stochastic dynamic optimization of epidemics
  23. Franziska Wollny (2021) - Bounds for the Expected Distance of Independent Samples From Random Vectors
  24. Chantal Klinkhammer (2021) - Simulation Methods for Generating Multivariate Extreme Value Distributed Random Numbers Based on Representations via Copulas and Point Processes
  25. Robin Mey (2022) - A Stochastic Model for Wind Data Based on Non-Stationary Time Series Analysis
  26. Toufik Ouhammou (2023) - Optimal Dividend Policies with Risk-Sensitive Preferences
  27. Ekaterina Sawatzky (2024) - Expectiles and Omega Ratio as Performance Measures for Portfolio Optimization
  28. Paul Hesse (2025) - Characterizations of Almost Stochastic Dominance

  1. Florian Bagus (2012) - Structural statements for the optimal exercise strategies for multiple stop problems and swing options
  2. Jan Müller (2013) - Stochastic Modeling of the Spot Price of Electricity Incorporating Commodities and Renewables as Exogenous Factors
  3. Kevin Berk (2016) - Probabilistic Forecasting of Electricity Load for Industrial Enterprises
  4. Matthias Reuber (2019) - Stochastic Models for Irradiations and Photovoltaic Yields
  5. Maximilian Stock (2022) - Investigations on the Discrimination Ability of Multivariate Scoring Rules

DAV Correspondence

Alfred Müller is a board member of the German Society for Actuarial and Financial Mathematics (DGVFM) and a correspondent of the German Actuarial Association (DAV) at the University of Siegen. One of his tasks is to inform students about training to become an actuary and about the actuarial profession. If you have any questions on this topic, you are welcome to make an appointment.

General information about the actuarial profession, actuarial training and possible internships can be found on the DAV website and on the "Become an actuary" website.

Applicants for admission to actuarial training can, under certain conditions, receive a certificate from Alfred Müller confirming that they have basic knowledge of probability theory and statistics. This certificate exempts them from the corresponding entrance examination. The required prior knowledge can be found in the DAV examination regulations.

The above-mentioned prior knowledge is usually acquired by successfully completing the modules Stochastics I and Stochastics II as well as a statistics module such as Statistical Analysis or Computational Statistics.

  • Actuaries are experts who use mathematical methods to evaluate financial uncertainties in the areas of insurance, pensions, investments and building society savings. After studying mathematics, actuaries also undergo training to become an actuary, usually as part of a job with an insurance company.

DAV website
"Become an actuary" website
DAV regulations