I maintain a list of Addenda and Corrigenda for my papers.

## Preprints

[46] M. Forde, S. Gerhold, B. Smith, *Small-time and large-time smile behaviour for the Rough Heston model,* 2019. Submitted. pdf

[45] S. Gerhold, C. Gerstenecker, *Large deviations related to the law of the iterated logarithm for Ito diffusions,* 2019. Submitted.
arXiv

[44] S. Gerhold, F. Hubalek, Ž. Tomovski, *Asymptotics of some generalized Mathieu series,* 2019. Submitted.
.pdf

[43] S. Gerhold, C. Gerstenecker, A. Pinter, * Moment explosions in the rough Heston model, * 2019. Submitted.
arXiv

## Refereed publications

[42] S. Gerhold, I. C. Gülüm, * Consistency of option prices under bid-ask
spreads, * 2019. To appear in Mathematical Finance.
arXiv

[41] S. Gerhold, A. Pinter, *Difference equation theory meets mathematical finance,* 2019. To appear in Peter Paule's 60th birthday Festschrift.
.pdf

[40] S. Gerhold, I. C. Gülüm, * Peacocks nearby: approximating sequences of measures, * Stochastic Processes
and their Applications 129(7), pp. 2406-2436, 2019.
.pdf

[39] S. Gerhold, P. Krühner, * Dynamic trading under integer constraints, * Finance and Stochastics 22(4), pp. 919-957, 2018.
open access

[38] P. Friz, S. Gerhold, A. Pinter, *Option Pricing in the Moderate Deviations Regime,*
Mathematical Finance 28(3), pp. 962-988, 2018.
open access

[37] S. Gerhold, I. C. Gülüm, A. Pinter, * Small-maturity asymptotics for the
at-the-money implied volatility slope in Lévy models,*
Applied Mathematical Finance 23(2), pp. 135–157, 2016.
.pdf

[36] S. Gerhold, M. Kleinert, P. Porkert, M. Shkolnikov,
*Small time central limit theorems for semimartingales with applications,*
Stochastics 87(5), pp. 723-746, 2015.
.pdf

[35] S. Gerhold,
*Small-maturity digital options in Lévy models: an analytic approach,*
Lithuanian Mathematical Journal 55(2), pp. 222-230, 2015.
.pdf

[34] S. Gerhold, J. Morgenbesser, A. Zrunek, *Refined wing asymptotics for the Merton and Kou jump diffusion
models,* Banach Center Publ. 104, pp. 85-94, 2015.
.pdf

[33] P. Friz, S. Gerhold, * Extrapolation analytics for Dupire's local volatility,* in:
Large Deviations and Asymptotic Methods in Finance
(Editors: P. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier, J. Teichmann),
Springer Proceedings in Mathematics and Statistics, Vol. 110, 2015.
pdf

[32] M. Drmota, S. Gerhold, *Disproof of a conjecture by Rademacher on partial fractions,*
Proc. Amer. Math. Soc. Ser. B 1, pp. 121–134, 2014.
.pdf

[31] P. Friz, S. Gerhold, M. Yor, * How to make Dupire's local volatility work with
jumps,* Quantitative Finance 14(8), pp. 1327-1331, 2014.
.pdf
corrigendum

[30] S. Gerhold, P. Guasoni, J. Muhle-Karbe, W. Schachermayer,
* Transaction Costs, Trading Volume, and the Liquidity Premium,*
Finance and Stochastics 18(1), pp. 1-37, 2014.
.pdf

[29] S. Altay, S. Gerhold, R. Haidinger, K. Hirhager,
* Digital double barrier options: Several barrier periods and structure floors,*
International Journal of Theoretical & Applied Finance 16(8), 14 pages, 2013.
.pdf

[28] S. Gerhold, * Can there be an explicit formula for implied volatility?*
Applied Mathematics E-Notes 13, pp. 17-24, 2013.
.pdf

[27] S. Gerhold, J. Muhle-Karbe, W. Schachermayer,
* The dual optimizer for the growth-optimal portfolio under transaction costs, *
Finance and Stochastics 17, pp. 325-354,
2013. .pdf
MathSciNet

[26] S. De Marco, P. Friz, S. Gerhold,
* Rational shapes of local volatility, * Risk, February 2013, pp. 82-87.
.pdf

[25] S. Gerhold, J. Muhle-Karbe, W. Schachermayer,
* Asymptotics and Duality for the Davis and Norman Problem, * Stochastics
84(5-6) (The Mark H.A. Davis festschrift), pp. 625-641, 2012.
.pdf

[24] S. Gerhold,
* Asymptotics for a variant of the Mittag-Leffler function, *
Integral Transforms and Special Functions 23(6), pp. 397-403, 2012.
.pdf

[23] S. Gerhold,
* The Hartman-Watson distribution revisited: asymptotics for pricing Asian
options, * J. Appl. Probab. 48(3), pp. 892-899, 2011.
.pdf

[22] P. Friz, S. Gerhold, A. Gulisashvili, S. Sturm,
* On Refined Volatility Smile Expansion in the Heston Model,*
Quantitative Finance 11(8), pp. 1151-1164, 2011.
.pdf

[21] S. Gerhold, * Counting Finite Languages by Total Word Length, *
INTEGERS 11, paper no. A44, 2011.
.pdf

[20] S. Gerhold,
* The Longstaff-Schwartz Algorithm for Lévy Models: Results on Fast and Slow Convergence,*
Annals of Applied Probability 21(2), pp. 589-608, 2011.
.pdf

[19] S. Gerhold,
* Moment Explosion in the LIBOR Market Model, *
Statistics & Probability Letters 81(5), pp. 560-562, 2011.
.pdf

[18] S. Gerhold, M. Zeiner,
* Convergence Properties of Kemp's q-Binomial Distribution,* Sankhya Series A 72(2), pp. 331-343, 2010.
.pdf

[17] A. Benoit, F. Chyzak, A. Darrasse, S. Gerhold, M. Mezzarobba, B. Salvy,
* The Dynamic Dictionary of Mathematical Functions (DDMF), *
In Komei Fukuda et al., editors,
The Third International Congress on Mathematical Software (ICMS 2010),
Lecture Notes in Computer Science, vol. 6327, pages 35-41, 2010.
.pdf

[16] S. Gerhold,
* Asymptotic Estimates for Some Number Theoretic Power Series,* Acta Arithmetica 142(2), pp. 187-196, 2010.
.pdf

[15] S. Gerhold,
* Unimodality of Two Distributions Related to the Negative Binomial Distribution,* Journal of Statistical Theory and
Applications 9(1), pp. 1-7, 2010.
.pdf

[14] S. Gerhold, U. Schmock, R. Warnung,
* A Generalization of Panjer's Recursion and Numerically Stable Risk Aggregation,* Finance and Stochastics 14, pp. 81-128,
2010. .pdf;
slightly corrected version;
slides by Uwe Schmock

[13] P. Flajolet, S. Gerhold, B. Salvy,
* Lindelöf Representations and (Non-)Holonomic Sequences,* Electronic Journal of Combinatorics 17(1), 2010.
.pdf

[12] S. Gerhold,
* The Shape of the Value Sets of Linear Recurrence Sequences,* Journal of Integer Sequences 12, 2009.
.pdf

[11] S. Gerhold,
* Asymptotic Analysis of Some Discrete Distributions by the Saddle Point Method,* Comm. Statist. Theory Methods 38(2), pp. 262-271, 2009.
.pdf

[10] S. Gerhold, R. Warnung,
* Finding Efficient Recursions for Risk Aggregation by Computer Algebra,* Journal of Computational
and Applied Mathematics 223, pp. 499-507, 2009.
.pdf

[9] J.P. Bell, S. Gerhold, M. Klazar, F. Luca,
* Non-Holonomicity of Sequences defined via Elementary Functions, * Annals of Combinatorics 12(1), pp. 1-16, 2008.
.pdf

[8] S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, B. Zimmermann,
* Computing the complexity for Schelling segregation models, * Communications in Nonlinear Science and Numerical Simulation 13(10),
pp. 2236-2245, 2008.
.pdf

[7] H. Alzer, S. Gerhold, M. Kauers, A. Lupas,
* On Turán's Inequality for Legendre Polynomials, * Expo. Math. 25(2), pp. 181-186, 2007.
.pdf

[6] J.P. Bell, S. Gerhold, * On the Positivity Set of a Linear Recurrence Sequence,*
Israel J. Math. 157, pp. 333-345, 2007.
.pdf

[5] S. Gerhold, M. Kauers, * A Computer Proof of Turán's Inequality, *
Journal of Inequalities in Pure and Applied Mathematics 7(2), 2006.
.pdf
.bib

[4] P. Flajolet, S. Gerhold, B. Salvy, * On the non-holonomic character of logarithms, powers and
the nth prime function,* Electronic Journal of Combinatorics 11(2), 2005.
.pdf
.bib

[3] S. Gerhold, M. Kauers, * A Procedure for Proving Special Function Inequalities Involving
a Discrete Parameter,* Proceedings of ISSAC '05, M. Kauers (ed.), ACM Press, pp. 156-162, 2005.
.pdf
.ps
.bib

[2] S. Gerhold, * Point Lattices and Oscillating Recurrence Sequences,*
Journal of Difference Equations and Applications 11(6), pp. 515-533, 2005.
.pdf
.bib

[1] S. Gerhold, *On Some Non-Holonomic Sequences,* Electronic Journal of Combinatorics 11(1), 2004.
.pdf
.bib

## Book chapter

[1] S. Gerhold, M. Kauers, C. Koutschan, P. Paule, C. Schneider, B. Zimmermann, * Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order,*
book chapter in: Schneider, Blümlein (Eds.),
Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions.
Springer, 2013.
arXiv
Springer

## Theses

[3] S. Gerhold, * Special Functions: From Lindelöf Integrals to Volatility Smiles,*
habilitation thesis, Vienna University of Technology, 2011.
slides

[2] S. Gerhold, * Combinatorial Sequences: Non-Holonomicity and Inequalities,* Ph.D. thesis,
J. Kepler University Linz, 2005.
.pdf
.bib

[1] S. Gerhold, * Uncoupling Systems of Linear Ore Operator Equations,* diploma thesis, J. Kepler University Linz, 2002.
.pdf
.ps
.bib
citations in physics papers

## Coauthors

So far I have had the pleasure to collaborate with the following 41 people. My Erdős number is 2, thanks to my coauthor Florian Luca.

Sühan Altay, Horst Alzer, Jason Bell, Alexandre Benoit, Frédéric Chyzak, Alexis Darrasse, Stefano De Marco, Michael Drmota, Paul Eisenberg, Philippe Flajolet †, Peter Friz, Lev Glebsky, Paolo Guasoni, Archil Gulisashvili, I. Cetin Gülüm, Rainer Haidinger, Karin Hirhager, Manuel Kauers, Martin Klazar, Maximilian Kleinert, Christoph Koutschan, Florian Luca, Alexandru Lupas † (Obituary), Marc Mezzarobba, Johannes Morgenbesser, Johannes Muhle-Karbe, Peter Paule, Arpad Pinter, Piet Porkert, Bruno Salvy, Walter Schachermayer, Uwe Schmock, Carsten Schneider, Mykhaylo Shkolnikov, Stephan Sturm, Richard Warnung, Marc Yor † (Obituary), Howie Weiss, Martin Zeiner, Burkhard Zimmermann, Axel Zrunek

## Selected talks

*Moment Explosions in the Rough Heston Model,*
Mar 15, 2018. Mathematical finance and related issues, Osaka.

* Dynamic trading under integer constraints,*
Sep 14, 2017. ÖMG - DMV 2017, Salzburg.

* Consistency of option prices under bid-ask spreads,*
Feb 27, 2017. Mathematics of quantitative finance, Oberwolfach.

* Option pricing in the moderate deviations regime, *
July 2016. 9th World Congress of the Bachelier Finance Society, NYC.
.pdf

*Small-maturity options in the moderate regime,* Sep 2015. Joint Austrian-Hungarian
Mathematical Conference, Győr.

*Utility maximization and symbolic computation,*
Jun 3, 2015. 13th International Symposium on Orthogonal Polynomials, Special Functions & Applications, NIST, Gaithersburg.

*The Small-Maturity Implied Volatility Slope for Lévy Models,*
Nov 14, 2014. SIAM Conference on Financial Mathematics & Engineering, Chicago.

*From Kellerer's Theorem to Local Volatility Models,*
Oct 31, 2014. Séminaire Bachelier, Paris.

* The Small-Maturity Implied Volatility Slope for Lévy Models, *
Jun 5, 2014. Eighth World Congress of the Bachelier Finance Society, Brussels.
.pdf

* Disproof of a conjecture by Rademacher on partial fractions, *
Apr 2, 2014. Mathematisches Kolloquium, Universität Wien.
.pdf

* Disproof of a conjecture by Rademacher on partial fractions, *
Jan 8, 2014. Algorithmic combinatorics seminar, RISC, JKU Linz.

* Local Volatility Models: Approximation and Regularization, *
Jun 11, 2013. Advances in Mathematics of Finance - 6th General AMaMeF and Banach Center Conference, Warsaw.
.pdf

* Local volatility asymptotics and small-time central limit theorems, *
Apr 9, 2013. Workshop on Large deviations and asymptotic methods in finance,
Imperial College London.
.pdf

* Small time central limit theorems for semimartingales with applications, *
Feb 13, 2013. Seminar talk at TU Berlin.
.pdf

* Some traces of discrete mathematics in mathematical finance, *
Jan 29, 2013.
Invited colloquium talk at the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria.
.pdf

* Extrapolation analytics for Dupire's local volatility, *
July 6, 2012. 6th European Congress of Mathematics, Krakow.
.pdf

* Don't stay local - extrapolation analytics for Dupire's local volatility, *
June 21, 2012. Seventh World Congress of the Bachelier Finance Society, Sydney.

* Utility maximization under transaction costs, *
May 30, 2012. 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics (OCDGND).

* Transaction costs, trading volume, and the liquidity premium, *
Mar 8, 2012. Stochastiktage Mainz 2012.
.pdf

* Transaction costs, trading volume, and the liquidity premium, *
Feb 3, 2012. Nomura seminar, University of Oxford.

* Transaction costs made tractable, *
Dec 14, 2011. QMF 2011, Sydney.

*On Refined Volatility Smile Expansion In The Heston Model, *
July 21, 2011. ICIAM 2011, Vancouver.
.pdf

* Special Functions: From Lindelöf Integrals to Volatility Smiles, *
June 28, 2011. Habilitationskolloquium, TU Wien.
.pdf

*On Refined Volatility Smile Expansion In The Heston Model, *
June 26, 2010. Sixth World Congress of the Bachelier Finance Society, Toronto.
.pdf

* Lindelöf integral representations and asymptotic analysis of a certain power series with closed-form coefficients, * January 20, 2009.
Colloquium talk at the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria.
.pdf

*Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for American Option Pricing,* October 18, 2008.
Invited talk at the Conference on Numerical Methods for American and Bermudan Options, Wolfgang Pauli Institute, Vienna (Austria).
.pdf

*On a Certain Functional Equation: Oscillations in the Solutions and Their Taylor Coefficients,* September 8, 2008.
Invited colloquium talk at INRIA Rocquencourt, France.
.pdf

*The Sign Structure of Linear Recurrence Sequences,*
Apr 1, 2007. Invited talk at Progress on Difference Equations 2007, Laufen, Germany.
.pdf

*Automatisches Beweisen von Identitäten,*
Oct 30, 2006. Colloquium talk, Wissenswertes aus der Mathematik, Vienna University of Technology, Austria.
.pdf

*An Implementation of the LIBOR Market Model for Pricing Exotic Constant Maturity Swaps,*
Sep 26, 2006. Invited talk at PRisMa 2006, Vienna University of Technology, Austria.

*An Implementation of the LIBOR Market Model,*
Aug 30, 2006. Seminar talk at the Research Unit of Financial and Actuarial Mathematics, Vienna University of Technology, Austria.

*Crashcourse Interest Rate Models,*
Aug 30, 2006. Seminar talk at the Research Unit of Financial and Actuarial Mathematics, Vienna University of Technology, Austria.
.pdf

*Non-Holonomic Sequences and Functions,*
May 16, 2006. Invited colloquium talk at the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria.
.pdf

*Special Functions: Applications of Computer Algebra in Stochastics,*
May 4, 2006. Colloquium talk at Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria.

*Special Functions: Applications of Computer Algebra in Stochastics,*
January 10, 2006. Invited colloquium talk at Vienna University of Technology, Austria.
.pdf

*Recurrence Relations and Inequalities,* November 14, 2005.
Invited colloquium talk at INRIA Rocquencourt, France.
.pdf

* Positivity of P-Recursive Sequences,* October 11, 2004.
Contributed talk at Séminaire Lotharingien de Combinatoire, Ellwangen, Germany.