I maintain a list of Addenda and Corrigenda for my papers.
Preprints
[28] S. Gerhold, P. Guasoni, J. Muhle-Karbe, W. Schachermayer,
Transaction Costs, Trading Volume, and the Liquidity Premium, 2012. Submitted.
arXiv
[27] P. Friz, S. Gerhold,
Don't stay local - extrapolation analytics for Dupire's local volatility, 2012. Submitted.
arXiv
Refereed Publications
[26] S. Gerhold, J. Muhle-Karbe, W. Schachermayer,
Asymptotics and Duality for the Davis and Norman Problem, 2012. To appear in Stochastics.
arXiv
[25] S. Gerhold,
Asymptotics for a variant of the Mittag-Leffler function, 2012. To appear in
Integral Transforms and Special Functions.
.pdf
[24] S. Gerhold, J. Muhle-Karbe, W. Schachermayer,
The dual optimizer for the growth-optimal portfolio under transaction costs, 2012. To appear
in Finance and Stochastics.
arXiv
[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
[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
Theses
[3] S. Gerhold, Special Functions: From Lindelöf Integrals to Volatility Smiles,
habilitation thesis, Vienna University of Technology, 2011.
.pdf
[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
Unpublished
[2] S. Gerhold, M. Kauers, F.W.J. Olver, P. Paule, C. Schneider, B. Zimmermann,
Computer Proofs of Some Identities Involving Derivatives of Bessel Functions With
Respect to Order, 2006. In preparation.
[1] S. Gerhold, M. Kauers, J. Schöberl,
On a Conjectured Inequality for a Sum of Legendre Polynomials.
Technical report, SFB F013, Johannes Kepler University Linz, 2006.
.pdf
Coauthors
So far I have had the pleasure to write joint papers with the following 20 people. My Erdős number is 2, thanks to my coauthor Florian Luca. It seems that his joint work with Paul Erdős is the last published Erdős-paper.
Horst Alzer
Jason Bell
Philippe Flajolet †
(Book of tribute)
Peter Friz
Lev Glebsky
Archil Gulisashvili
Manuel Kauers
Martin Klazar
Florian Luca
Alexandru Lupas †
Johannes Muhle-Karbe
Bruno Salvy
Walter Schachermayer
Uwe Schmock
Carsten Schneider
Stephan Sturm
Richard Warnung
Howie Weiss
Martin Zeiner
Burkhard Zimmermann
Selected Talks
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.