Apl. Prof. Dr. Frederik Herzberg

Publications

Research monographs

• F.S. Herzberg, Stochastic calculus with infinitesimals. 
  Lecture Notes in Mathematics, vol. 2067, Springer, Heidelberg, 2013. — Corrigenda
• S. Albeverio, R.Z. Fan & F.S. Herzberg, Hyperfinite Dirichlet forms and stochastic processes. 
  Lecture Notes of the Unione Matematica Italiana, vol. 10, Springer, Heidelberg, 2011.

Edited special issue

• F.S. Herzberg & D. von Wachter (eds.), Causality and Action, special issue of Organon F 26 (2019), no. 1.

Articles in refereed journals and refereed proceedings volumes

Mathematical papers

• T.R. Fadina & F.S. Herzberg, "Hyperfinite construction of G-expectation". 
  Stochastics 91 (2019), no. 1, pp. 52–66. doi:10.1080/17442508.2018.1502771
• F.S. Herzberg, V. Kanovei, M. Katz & V. Lyubetsky, "Minimal axiomatic frameworks for definable hyperreals with transfer". 
  Journal of Symbolic Logic 83 (2018), no. 1, pp. 385–391. doi:10.1017/jsl.2017.48
• T. Bascelli, E. Bottazzi, F.S. Herzberg, V. Kanovei, K.U. Katz, M.G. Katz, T. Nowik, D. Sherry & S. Shnider,
  "Fermat, Leibniz, Euler, and the Gang: The True History of the Concepts of Limit and Shadow". 
  Notices of the American Mathematical Society 61 (2014), no. 8, pp. 848–864. doi:10.1090/noti1149
• F.S. Herzberg, "Simple nonstandard proofs of Daniell—Kolmogorov-type theorems". 
  Positivity 16 (2012), no. 4, pp. 627–631. doi:10.1007/s11117-011-0135-7
• F.S. Herzberg, "Hyperfinite stochastic integration for Lévy processes with finite-variation jump part". 
  Bulletin des Sciences Mathématiques 134 (2010), no. 4, pp. 423–445. doi:10.1016/j.bulsci.2010.02.004
• F.S. Herzberg & T. Lindstrøm, "Corrigendum and addendum to ‘Hyperfinite Lévy processes’ by Tom Lindstrøm". 
  Stochastics 81 (2009), no. 6, pp. 567–570. doi:10.1080/17442500902998615
• F.S. Herzberg, "Perpetual Bermudan continuity corrections and a multi-dimensional Wiener-Hopf type result". 
  Stochastic Analysis and Applications 27 (2009), no. 1, pp. 176–195. doi:10.1080/07362990802405703
• F.S. Herzberg, "Addendum to ‘A definable nonstandard enlargement’ ". 
  Mathematical Logic Quarterly 54 (2008), no. 6, pp. 666–667. doi:10.1002/malq.200810002
• F.S. Herzberg, "A definable nonstandard enlargement". 
  Mathematical Logic Quarterly 54 (2008), no. 2, pp. 167–175. doi:10.1002/malq.200710022
• S. Albeverio & F.S. Herzberg, "Optimisation of measures on a hyperfinite adapted probability space". 
  Acta Applicandae Mathematicae 100 (2008), no. 1, pp. 1–14. doi:10.1007/s10440-007-9174-2
• S. Albeverio & F.S. Herzberg, "The moment problem on the Wiener space". 
  Bulletin des Sciences Mathématiques 132 (2008), no. 1, pp. 7–18. doi:10.1016/j.bulsci.2007.01.002
• F.S. Herzberg, "On two recent applications of nonstandard analysis to the theory of financial markets".
  In: The Strength of Nonstandard Analysis. Proceedings of the International Conference on Nonstandard Mathematics, Aveiro, Portugal, June 2004 (eds. I. van den Berg and V. Neves, preface by W.A.J. Luxemburg), Springer, Vienna 2007, pp. 177–188. doi:10.1007/978-3-211-49905-4
• S. Albeverio & F.S. Herzberg, "A combinatorial infinitesimal representation of Lévy processes". 
  Stochastics 78 (2006), no. 5, pp. 301–325. doi:10.1080/17442500600900707
• S. Albeverio & F.S. Herzberg, "Lifting Lévy processes to hyperfinite random walks". 
  Bulletin des Sciences Mathématiques 130 (2006), no. 8, pp. 697–706. doi:10.1016/j.bulsci.2006.02.001

Philosophical papers

• F.S. Herzberg, "Arrovian aggregation of generalised expected-utility preferences". 
  Studia Logica 106 (2018), no. 5, pp. 947–967. doi:10.1007/s11225-016-9706-8
• D. Eckert & F.S. Herzberg, "The birth of social choice theory from the spirit of mathematical logic". 
  Studia Logica 106 (2018), no. 5, pp. 893–911. doi:10.1007/s11225-018-9794-8
• F.S. Herzberg, "A note on ‘The No Alternatives Argument’ by Richard Dawid, Stephan Hartmann and Jan Sprenger". 
  European Journal for Philosophy of Science 4 (2014), no. 3, pp. 375–384. doi:10.1007/s13194-014-0092-7
• F.S. Herzberg, "A graded Bayesian coherence notion". 
  Erkenntnis 79 (2014), no. 4, pp. 843–869. doi:10.1007/s10670-013-9569-6
• F.S. Herzberg, "The dialectics of infinitism and coherentism: Inferential justification versus holism and coherence". 
  Synthese 191 (2014), no. 4, pp. 701–723. doi:10.1007/s11229-013-0273-5
• F.S. Herzberg, "The consistency of probabilistic regresses: Some implications for epistemological infinitism". 
  Erkenntnis 78 (2013), no. 2, pp. 371–382. doi:10.1007/s10670-011-9358-z
• F.S. Herzberg & D. Eckert, "Impossibility results for infinite-electorate abstract aggregation rules". 
  Journal of Philosophical Logic 41 (2012), no. 1, pp. 273–286. doi:10.1007/s10992-011-9203-5
• F.S. Herzberg, "Hyperreal expected utilities and Pascal's Wager". 
  Logique et Analyse 54 (2011), no. 213, pp. 69–108.
• F.S. Herzberg, "The consistency of probabilistic regresses. A reply to Jeanne Peijnenburg and David Atkinson". 
  Studia Logica 94 (2010), no. 3, pp. 331–345. doi:10.1007/s11225-010-9242-x
• F.S. Herzberg, "Internal laws of probability, generalized likelihoods and Lewis' infinitesimal chances – a response to Adam Elga". 
  British Journal for the Philosophy of Science 58 (2007), no. 1, pp. 25–43. doi:10.1093/bjps/axl028

Economics papers

• F.S. Herzberg, "Corrigendum to ‘Respect for experts vs. respect for unanimity’". 
  Economics Letters 205 (2021), pp. 109964. doi:10.1016/j.econlet.2021.109964
• F.S. Herzberg, "Respect for experts vs. respect for unanimity: The liberal paradox in probabilistic opinion pooling". 
  Economics Letters 151 (2017), pp. 44–47. doi:10.1016/j.econlet.2016.12.012
• F.S. Herzberg, "Aggregating infinitely many probability measures". 
  Theory and Decision 78 (2015), no. 2, pp. 319–337. doi:10.1007/s11238-014-9424-5
• L. Goerke, F.S. Herzberg & T. Upmann, "Failure of ad valorem and specific tax equivalence under uncertainty". 
  International Journal of Economic Theory 10 (2014), no. 4, pp. 387–402. doi:10.1111/ijet.12046
• F. Riedel & F.S. Herzberg, "Existence of financial equilibria in continuous time with potentially complete markets". 
  Journal of Mathematical Economics 49 (2013), no. 5, pp. 398–404. doi:10.1016/j.jmateco.2013.07.001
• F.S. Herzberg, "First steps towards an equilibrium theory for Lévy financial markets". 
  Annals of Finance 9 (2013), no. 3, pp. 543–572. doi:10.1007/s10436-012-0202-5
• F.S. Herzberg, "The (im)possibility of collective risk measurement: Arrovian aggregation of variational preferences". 
  Economic Theory Bulletin 1 (2013), no. 1, pp. 69–92. doi:10.1007/s40505-013-0004-6
• F.S. Herzberg & D. Eckert, "The model-theoretic approach to aggregation: Impossibility results for finite and infinite electorates". 
  Mathematical Social Sciences 64 (2012), no. 1, pp. 41–47. doi:10.1016/j.mathsocsci.2011.08.004
• F.S. Herzberg, "A representative individual from Arrovian aggregation of parametric individual utilities". 
  Journal of Mathematical Economics 46 (2010), no. 6, pp. 1115–1124. doi:10.1016/j.jmateco.2010.10.002
• F.S. Herzberg, L. Lauwers, L. Van Liedekerke & E.S. Fianu,
  "Addendum to L. Lauwers and L. Van Liedekerke, ‘Ultraproducts and aggregation’ ". 
  Journal of Mathematical Economics 46 (2010), no. 2, pp. 277–278. doi:10.1016/j.jmateco.2009.06.001
• F.S. Herzberg, "Judgment aggregators and Boolean algebra homomorphisms". 
  Journal of Mathematical Economics 46 (2010), no. 1, pp. 132–140. doi:10.1016/j.jmateco.2009.06.002
• F.S. Herzberg, "Elementary non-Archimedean utility theory". 
  Mathematical Social Sciences 58 (2009), no. 1, pp. 8–14. doi:10.1016/j.mathsocsci.2008.12.009
• F.S. Herzberg, "Black-Scholes theory for an underlying with multiple attractors". 
  Quantitative Finance 8 (2008), no. 5, pp. 453–457. doi:10.1080/14697680701518035

Papers on Artificial Intelligence

• F.S. Herzberg, "Corrigendum and addendum to ‘Universal algebra for general aggregation theory’". 
  Journal of Logic and Computation 25 (2015), no. 3, pp. 979–982. doi:10.1093/logcom/exv015
• F.S. Herzberg, "Universal algebra for general aggregation theory". 
  Journal of Logic and Computation 25 (2015), no. 3, pp. 965–977. doi:10.1093/logcom/ext009
• D. Eckert & F.S. Herzberg, "The Problem of Judgment Aggregation in the Framework of Boolean-Valued Models".
  In: Computational Logic in Multi-Agent Systems. CLIMA XV, August 2014, Proceedings (eds. N. Bulling, L. van der Torre, S. Villata, W. Jamroga, W. Vasconcelos), Lecture Notes in Computer Science, vol. 8624, Springer, Heidelberg, 2014, pp. 138–147. doi:10.1007/978-3-319-09764-0_9

Statistical papers

• F.S. Herzberg & A. Herzberg, "Testing fiscal sustainability via strong convergence of Gaussian random variables". 
  Communications in Statistics – Theory and Methods 42 (2013), no. 18, pp. 2535–2542. doi:10.1080/03610926.2011.622844
• F.S. Herzberg, "Value-at-Risk levels implied by risk estimators drawn from historical data". 
  Journal of Risk Model Validation 4 (2010), no. 3, pp. 3–26.
• F.S. Herzberg & C. Bennemann, "Order statistics for Value-at-Risk estimation and option pricing". 
  Wilmott Magazine no. 26 (2006), pp. 46–50. — Corrigendum
• B. Naundorf, J. Raufeisen, C. Bennemann & F.S. Herzberg,
  "You can't always get what you want – estimating the Value-at-Risk from historical data with limited statistics". 
  Wilmott Magazine no. 26 (2006), pp. 52–55.

Curriculum vitae

Academic qualifications

• Titular Professor [apl. Prof.], Bielefeld University 2016
• Habilitation for Philosophy, University of Munich [LMU] 2017
• Habilitation for Economic Theory, Bielefeld University 2011
• Doctorate [DPhil] in Mathematics, University of Oxford 2006;
  Specialisation: Mathematical Finance
• Doctorate [Dr.rer.nat.] in Mathematics, University of Bonn 2005;
  Specialisation: Probability Theory
• Master's equiv. [Diplom] in Mathematics, University of Bonn 2003
• Master of Theology, University of Aberdeen 2018

Employment history

• Lecturer [StR i.H.], Department of Mathematics, Saarland University, since 2022
• Research Fellow, Center for Mathematical Economics [IMW], Bielefeld University, 2022
• Secondary School Teacher (Mathematics, Business Administration & Economics), 2020–2022
• Research Fellow, International Academy of Philosophy [IAP] Liechtenstein, 2017–2019
• Program Officer, German Academic Scholarship Foundation, Bonn, 2015–2017
• Assistant Professor, Center for Mathematical Economics [IMW], Bielefeld University, 2007–2015
  • Visiting Fellow, Munich Center for Mathematical Philosophy [MCMP], University of Munich, 2012–2013
  • Visiting Fellow, Department of Mathematics, Princeton University, 2009–2010
  • Visiting Scholar, Department of Mathematics, University of California, Berkeley, 2008
• Post-Doctoral Researcher & Instructor, Institute for Applied Mathematics, University of Bonn, 2006–2007
• Consultant (Risk Management), d-fine GmbH, Frankfurt am Main, 2006
• Post-Doctoral Researcher & Instructor, Institute for Applied Mathematics, University of Bonn, 2005–2006

Scholarships & grants 

• International Academy of Philosophy [IAP] Liechtenstein / John Templeton Foundation: research fellowship (2017–2019)
• Munich Center for Mathematical Philosophy [MCMP] / Alexander von Humboldt Foundation: research fellowship (2012–2013)
• Center for Interdisciplinary Research [ZiF] Bielefeld: Network of Young Scholars membership (2011–2013)
• German Research Foundation [DFG]: research fellowship (Princeton University, 2009–2010)
• German Academic Exchange Service [DAAD]: research fellowship (University of California, Berkeley, 2008)
• German Academic Exchange Service [DAAD]: pre-doctoral scholarship (University of Oxford, 2004–2005)
• German Academic Scholarship Foundation [Studienstiftung des deutschen Volkes]: undergraduate and pre-doctoral scholarship 2000–2004

Other distinctions

Shortlisted for permanent professorships at the University of Würzburg (Institute of Mathematics, 2009) and other universities.

Doctoral students

• Geghard Bedrosian (2012–2015)
• Tolulope Fadina (2011–2015)

Academic service (selection)

• Reviewer for grant applications with the European Research Council [ERC], Austrian Academy of Sciences [OeAW],  German Academic Scholarship Foundation and Evangelisches Studienwerk Villigst 
• Reviewer for Zentralblatt MATH and Mathematical Reviews
• Referee for various academic journals and publishers, including
  • Advances in Mathematics, Finance and Stochastics, Journal of Mathematical Analysis and Applications, Journal of Nonparametric Statistics, Physica A: Statistical Mechanics and its Applications, Stochastic Processes and their Applications, Studia Logica, 
  • Economic Theory, Economics Letters, Journal of Mathematical Economics, Macroeconomic Dynamics, Mathematics and Financial Economics, Quantitative Finance, Review of Economic Design, 
  • Archiv für Geschichte der Philosophie, Dialectica, Economics and Philosophy, Erkenntnis, Foundations of Science, Journal of Philosophical Logic, MIND, Philosophia Mathematica, Review of Symbolic Logic, Synthese,
  • Routledge CRC Press
• Deputy Member, Ethics Committee, Bielefeld University, 2014–2022
• Program Committee Member, Trends in Logic XV, Delft, 2015
• Scientific Co-Organizer (with A. Kurz & A. Palmigiano), Lorentz Center Workshop “Logics for Social Behaviour”, Leiden 2014