## Gerhold, Stefan

Compute Distance To:
 Author ID: gerhold.stefan Published as: Gerhold, Stefan; Gerhold, S. External Links: MGP
 Documents Indexed: 50 Publications since 2004 Reviewing Activity: 7 Reviews Co-Authors: 49 Co-Authors with 36 Joint Publications 1,480 Co-Co-Authors
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### Co-Authors

 14 single-authored 4 Friz, Peter Karl 4 Kauers, Manuel 4 Pinter, Arpad 3 Gerstenecker, Christoph 3 Gülüm, Ismail Cetin 3 Muhle-Karbe, Johannes 3 Salvy, Bruno 3 Schachermayer, Walter 2 Bell, Jason P. 2 Flajolet, Philippe 2 Gulisashvili, Archil 2 Schneider, Carsten 2 Tomovski, Živorad 2 Warnung, Richard 2 Zimmermann, Burkhard 1 Altay, Sühan 1 Alzer, Horst 1 Benoit, Alexandre 1 Chyzak, Frédéric 1 Darrasse, Alexis 1 Drmota, Michael 1 Forde, Martin 1 Fukasawa, Masaaki 1 Glebsky, Lev Yu. 1 Guasoni, Paolo 1 Haidinger, Rainer 1 Hirhager, Karin 1 Hubalek, Friedrich 1 Jacquier, Antoine 1 Klazar, Martin 1 Kleinert, Max 1 Koutschan, Christoph 1 Krühner, Paul 1 Luca, Florian 1 Lupaş, Alexandru 1 Mezzarobba, Marc 1 Morgenbesser, Johannes F. 1 Pakkanen, Mikko S. 1 Paule, Peter 1 Porkert, Piet 1 Schmock, Uwe 1 Shkolnikov, Mykhaylo 1 Stone, Henry 1 Sturm, Stephan 1 Wagenhofer, Thomas 1 Weiss, Howard 1 Yor, Marc 1 Zeiner, Martin 1 Zrunek, Axel
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### Serials

 4 Finance and Stochastics 3 The Electronic Journal of Combinatorics 2 Journal of Applied Probability 2 Statistics & Probability Letters 2 Stochastic Processes and their Applications 2 Mathematical Finance 2 Quantitative Finance 2 Stochastics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Lithuanian Mathematical Journal 1 Mathematische Semesterberichte 1 Acta Arithmetica 1 Journal of Computational and Applied Mathematics 1 Mathematica Scandinavica 1 The Annals of Applied Probability 1 Communications in Statistics. Theory and Methods 1 Expositiones Mathematicae 1 Integral Transforms and Special Functions 1 Applied Mathematical Finance 1 Journal of Difference Equations and Applications 1 Electronic Communications in Probability 1 Mathematical Communications 1 Annals of Combinatorics 1 International Journal of Theoretical and Applied Finance 1 Journal of Integer Sequences 1 Communications in Nonlinear Science and Numerical Simulation 1 JIPAM. Journal of Inequalities in Pure & Applied Mathematics 1 Integers 1 Applied Mathematics E-Notes 1 Decisions in Economics and Finance 1 Sankhyā. Series A 1 Proceedings of the American Mathematical Society. Series B
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### Fields

 24 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Probability theory and stochastic processes (60-XX) 11 Special functions (33-XX) 9 Number theory (11-XX) 6 Statistics (62-XX) 5 Computer science (68-XX) 4 Combinatorics (05-XX) 4 Approximations and expansions (41-XX) 3 Real functions (26-XX) 2 Measure and integration (28-XX) 2 Functions of a complex variable (30-XX) 1 General and overarching topics; collections (00-XX) 1 Partial differential equations (35-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

39 Publications have been cited 270 times in 208 Documents Cited by Year
Gerhold, Stefan; Guasoni, Paolo; Muhle-Karbe, Johannes; Schachermayer, Walter
2014
On refined volatility smile expansion in the Heston model. Zbl 1267.91068
Friz, Peter; Gerhold, Stefan; Gulisashvili, Archil; Sturm, Stephan
2011
The dual optimizer for the growth-optimal portfolio under transaction costs. Zbl 1319.91142
Gerhold, S.; Muhle-Karbe, J.; Schachermayer, W.
2013
Asymptotics and duality for the Davis and Norman problem. Zbl 1276.91093
Gerhold, Stefan; Muhle-Karbe, Johannes; Schachermayer, Walter
2012
A procedure for proving special function inequalities involving a discrete parameter. Zbl 1360.68933
Gerhold, Stefan; Kauers, Manuel
2005
Asymptotics for a variant of the Mittag-Leffler function. Zbl 1257.33050
Gerhold, Stefan
2012
On the non-holonomic character of logarithms, powers, and the $$n$$th prime function. Zbl 1076.05004
Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno
2005
On Turán’s inequality for Legendre polynomials. Zbl 1155.26012
Alzer, Horst; Gerhold, Stefan; Kauers, Manuel; Lupaş, Alexandru
2007
Option pricing in the moderate deviations regime. Zbl 1411.91554
Friz, Peter; Gerhold, Stefan; Pinter, Arpad
2018
How to make Dupire’s local volatility work with jumps. Zbl 1402.91776
Friz, Peter K.; Gerhold, Stefan; Yor, Marc
2014
On the positivity set of a linear recurrence sequence. Zbl 1139.11010
Bell, Jason P.; Gerhold, Stefan
2007
Moment explosions in the rough Heston model. Zbl 1432.91123
Gerhold, Stefan; Gerstenecker, Christoph; Pinter, Arpad
2019
The longstaff-Schwartz algorithm for Lévy models: results on fast and slow convergence. Zbl 1219.62161
Gerhold, Stefan
2011
Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models. Zbl 1396.91731
Gerhold, Stefan; Gülüm, I. Cetin; Pinter, Arpad
2016
Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007
Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian
2008
A generalization of Panjer’s recursion and numerically stable risk aggregation. Zbl 1224.91060
Gerhold, Stefan; Schmock, Uwe; Warnung, Richard
2010
Lindelöf representations and (non-)holonomic sequences. Zbl 1222.05005
Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno
2010
Disproof of a conjecture by Rademacher on partial fractions. Zbl 1339.11087
Drmota, Michael; Gerhold, Stefan
2014
A computer proof of Turán’s inequality. Zbl 1132.26336
Gerhold, Stefan; Kauers, Manuel
2006
The Hartman-Watson distribution revisited: asymptotics for pricing Asian options. Zbl 1279.62041
Gerhold, Stefan
2011
Extrapolation analytics for Dupire’s local volatility. Zbl 1418.91511
Friz, Peter; Gerhold, Stefan
2015
On some non-holonomic sequences. Zbl 1063.11007
Gerhold, Stefan
2004
Point lattices and oscillating recurrence sequences. Zbl 1204.11024
Gerhold, Stefan
2005
The dynamic dictionary of mathematical functions (DDMF). Zbl 1295.65022
Benoit, Alexandre; Chyzak, Frédéric; Darrasse, Alexis; Gerhold, Stefan; Mezzarobba, Marc; Salvy, Bruno
2010
Moment explosion in the LIBOR market model. Zbl 1208.91152
Gerhold, Stefan
2011
Asymptotic estimates for some number-theoretic power series. Zbl 1206.11116
Gerhold, Stefan
2010
Can there be an explicit formula for implied volatility? Zbl 1315.91062
Gerhold, Stefan
2013
Counting finite languages by total word length. Zbl 1234.05024
Gerhold, Stefan
2011
Asymptotic expansion of Mathieu power series and trigonometric Mathieu series. Zbl 1450.30006
2019
Finding efficient recursions for risk aggregation by computer algebra. Zbl 1153.91592
Gerhold, Stefan; Warnung, Richard
2009
Small time central limit theorems for semimartingales with applications. Zbl 1337.60020
Gerhold, Stefan; Kleinert, Max; Porkert, Piet; Shkolnikov, Mykhaylo
2015
Refined wing asymptotics for the Merton and Kou jump diffusion models. Zbl 1312.91087
Gerhold, Stefan; Morgenbesser, Johannes F.; Zrunek, Axel
2015
Small-maturity digital options in Lévy models: an analytic approach. Zbl 1321.60093
Gerhold, Stefan
2015
Computing the complexity for Schelling segregation models. Zbl 1221.37185
Gerhold, Stefan; Glebsky, Lev; Schneider, Carsten; Weiss, Howard; Zimmermann, Burkhard
2008
Gerhold, Stefan; Gülüm, Ismail Cetin
2020
Asymptotic analysis of a double integral occurring in the rough Bergomi model. Zbl 1454.41012
Gerhold, Stefan
2020
Peacocks nearby: approximating sequences of measures. Zbl 1478.60012
Gerhold, Stefan; Gülüm, I. Cetin
2019
Convergence properties of Kemp’s $$q$$-binomial distribution. Zbl 1213.60045
Gerhold, Stefan; Zeiner, Martin
2010
The Riemann-Liouville field and its GMC as $$H \to 0$$, and skew flattening for the rough Bergomi model. Zbl 1478.60152
Forde, Martin; Fukasawa, Masaaki; Gerhold, Stefan; Smith, Benjamin
2022
The Riemann-Liouville field and its GMC as $$H \to 0$$, and skew flattening for the rough Bergomi model. Zbl 1478.60152
Forde, Martin; Fukasawa, Masaaki; Gerhold, Stefan; Smith, Benjamin
2022
Gerhold, Stefan; Gülüm, Ismail Cetin
2020
Asymptotic analysis of a double integral occurring in the rough Bergomi model. Zbl 1454.41012
Gerhold, Stefan
2020
Moment explosions in the rough Heston model. Zbl 1432.91123
Gerhold, Stefan; Gerstenecker, Christoph; Pinter, Arpad
2019
Asymptotic expansion of Mathieu power series and trigonometric Mathieu series. Zbl 1450.30006
2019
Peacocks nearby: approximating sequences of measures. Zbl 1478.60012
Gerhold, Stefan; Gülüm, I. Cetin
2019
Option pricing in the moderate deviations regime. Zbl 1411.91554
Friz, Peter; Gerhold, Stefan; Pinter, Arpad
2018
Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models. Zbl 1396.91731
Gerhold, Stefan; Gülüm, I. Cetin; Pinter, Arpad
2016
Extrapolation analytics for Dupire’s local volatility. Zbl 1418.91511
Friz, Peter; Gerhold, Stefan
2015
Small time central limit theorems for semimartingales with applications. Zbl 1337.60020
Gerhold, Stefan; Kleinert, Max; Porkert, Piet; Shkolnikov, Mykhaylo
2015
Refined wing asymptotics for the Merton and Kou jump diffusion models. Zbl 1312.91087
Gerhold, Stefan; Morgenbesser, Johannes F.; Zrunek, Axel
2015
Small-maturity digital options in Lévy models: an analytic approach. Zbl 1321.60093
Gerhold, Stefan
2015
Gerhold, Stefan; Guasoni, Paolo; Muhle-Karbe, Johannes; Schachermayer, Walter
2014
How to make Dupire’s local volatility work with jumps. Zbl 1402.91776
Friz, Peter K.; Gerhold, Stefan; Yor, Marc
2014
Disproof of a conjecture by Rademacher on partial fractions. Zbl 1339.11087
Drmota, Michael; Gerhold, Stefan
2014
The dual optimizer for the growth-optimal portfolio under transaction costs. Zbl 1319.91142
Gerhold, S.; Muhle-Karbe, J.; Schachermayer, W.
2013
Can there be an explicit formula for implied volatility? Zbl 1315.91062
Gerhold, Stefan
2013
Asymptotics and duality for the Davis and Norman problem. Zbl 1276.91093
Gerhold, Stefan; Muhle-Karbe, Johannes; Schachermayer, Walter
2012
Asymptotics for a variant of the Mittag-Leffler function. Zbl 1257.33050
Gerhold, Stefan
2012
On refined volatility smile expansion in the Heston model. Zbl 1267.91068
Friz, Peter; Gerhold, Stefan; Gulisashvili, Archil; Sturm, Stephan
2011
The longstaff-Schwartz algorithm for Lévy models: results on fast and slow convergence. Zbl 1219.62161
Gerhold, Stefan
2011
The Hartman-Watson distribution revisited: asymptotics for pricing Asian options. Zbl 1279.62041
Gerhold, Stefan
2011
Moment explosion in the LIBOR market model. Zbl 1208.91152
Gerhold, Stefan
2011
Counting finite languages by total word length. Zbl 1234.05024
Gerhold, Stefan
2011
A generalization of Panjer’s recursion and numerically stable risk aggregation. Zbl 1224.91060
Gerhold, Stefan; Schmock, Uwe; Warnung, Richard
2010
Lindelöf representations and (non-)holonomic sequences. Zbl 1222.05005
Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno
2010
The dynamic dictionary of mathematical functions (DDMF). Zbl 1295.65022
Benoit, Alexandre; Chyzak, Frédéric; Darrasse, Alexis; Gerhold, Stefan; Mezzarobba, Marc; Salvy, Bruno
2010
Asymptotic estimates for some number-theoretic power series. Zbl 1206.11116
Gerhold, Stefan
2010
Convergence properties of Kemp’s $$q$$-binomial distribution. Zbl 1213.60045
Gerhold, Stefan; Zeiner, Martin
2010
Finding efficient recursions for risk aggregation by computer algebra. Zbl 1153.91592
Gerhold, Stefan; Warnung, Richard
2009
Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007
Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian
2008
Computing the complexity for Schelling segregation models. Zbl 1221.37185
Gerhold, Stefan; Glebsky, Lev; Schneider, Carsten; Weiss, Howard; Zimmermann, Burkhard
2008
On Turán’s inequality for Legendre polynomials. Zbl 1155.26012
Alzer, Horst; Gerhold, Stefan; Kauers, Manuel; Lupaş, Alexandru
2007
On the positivity set of a linear recurrence sequence. Zbl 1139.11010
Bell, Jason P.; Gerhold, Stefan
2007
A computer proof of Turán’s inequality. Zbl 1132.26336
Gerhold, Stefan; Kauers, Manuel
2006
A procedure for proving special function inequalities involving a discrete parameter. Zbl 1360.68933
Gerhold, Stefan; Kauers, Manuel
2005
On the non-holonomic character of logarithms, powers, and the $$n$$th prime function. Zbl 1076.05004
Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno
2005
Point lattices and oscillating recurrence sequences. Zbl 1204.11024
Gerhold, Stefan
2005
On some non-holonomic sequences. Zbl 1063.11007
Gerhold, Stefan
2004
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### Cited by 310 Authors

 16 Gerhold, Stefan 12 Jacquier, Antoine 12 Muhle-Karbe, Johannes 9 Friz, Peter Karl 7 Guasoni, Paolo 7 Kauers, Manuel 5 Forde, Martin 5 Gulisashvili, Archil 5 Pillwein, Veronika 5 Schachermayer, Walter 4 Baricz, Árpád 4 Fukasawa, Masaaki 4 Lorig, Matthew J. 4 O’Sullivan, Cormac 4 Pagliarani, Stefano 4 Pascucci, Andrea 4 Pinter, Arpad 4 Pirjol, Dan 3 Bouchard, Bruno 3 Han, Bingyan 3 Herdegen, Martin 3 Kallsen, Jan 3 Pigato, Paolo 3 Soner, Halil Mete 3 Tomovski, Živorad 3 Wong, Hoi Ying 3 Yang, Junjian 3 Zanger, Daniel Z. 2 Altarovici, Albert 2 Alzer, Horst 2 Bayer, Christian 2 Belak, Christoph 2 Bell, Jason P. 2 Bichuch, Maxim 2 Bostan, Alin 2 Chen, Shaoshi 2 Czichowsky, Christoph 2 De Marco, Stefano 2 Desmettre, Sascha 2 Deuschel, Jean-Dominique 2 Dolinsky, Yan 2 Gassiat, Paul 2 Gatheral, Jim 2 Horvath, Blanka 2 Jakubowski, Jacek 2 Jiménez-Pastor, Antonio 2 Knopova, Victoria Pavlovna 2 Lin, Yiqing 2 Luca, Florian 2 Matic, Ivan 2 Radoičić, Radoš 2 Rogosin, Sergei V. 2 Roome, Patrick 2 Salvy, Bruno 2 Sass, Jörn 2 Shi, Fangwei 2 Stefanica, Dan 2 Violante, S. 2 Weber, Marko Hans 2 Wiśniewolski, Maciej 1 Abbas-Turki, Lokman A. 1 Aguilar, Jean-Philippe 1 Akel, Mohamed S. 1 Allaj, Erindi 1 Allouche, Jean-Paul Simon 1 Alonso, Ricardo J. 1 Andersen, Lars Nørvang 1 Asmussen, Søren 1 Balan, Raluca M. 1 Bank, Peter 1 Bansal, Manish Kumar 1 Bäuerle, Nicole 1 Baviera, Roberto 1 Bayraktar, Erhan 1 Beaton, Nicholas R. 1 Beghin, Luisa 1 Benedetti, Giuseppe 1 Bensoussan, Alain 1 Berg, Christian 1 Berthomieu, Jérémy 1 Bogdan, Krzysztof 1 Bóna, Miklós 1 Bruin, Nils 1 Byszewski, Jakub 1 Callegaro, Giorgia 1 Campi, Luciano 1 Caravenna, Francesco 1 Carrizosa, Emilio 1 Ceballos, Manuel 1 Cha, Yongjae 1 Chakraborty, Subrata 1 Chau, Huy N. 1 Chen, William Yong-Chuan 1 Choi, Jin Hyuk 1 Cohen, Samuel N. 1 Conus, Daniel 1 Coons, Michael 1 Corbetta, Jacopo 1 Cordwell, Katherine 1 Cornelissen, Gunther ...and 210 more Authors
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### Cited in 91 Serials

 17 Finance and Stochastics 14 SIAM Journal on Financial Mathematics 12 Quantitative Finance 10 International Journal of Theoretical and Applied Finance 9 Mathematical Finance 6 Journal of Symbolic Computation 5 Stochastic Processes and their Applications 4 Advances in Applied Mathematics 4 The Annals of Applied Probability 4 Integral Transforms and Special Functions 4 Applied Mathematical Finance 4 Stochastics 3 Journal of Computational and Applied Mathematics 3 Journal of Number Theory 3 SIAM Journal on Control and Optimization 2 Bulletin of the Australian Mathematical Society 2 Communications on Pure and Applied Mathematics 2 Discrete Applied Mathematics 2 Journal of Mathematical Analysis and Applications 2 Applied Mathematics and Computation 2 Applied Mathematics and Optimization 2 Journal of Applied Probability 2 Journal of Approximation Theory 2 Mathematics of Operations Research 2 Proceedings of the American Mathematical Society 2 Statistics & Probability Letters 2 Stochastic Analysis and Applications 2 Expositiones Mathematicae 2 Potential Analysis 2 International Journal of Number Theory 2 Frontiers of Mathematics in China 2 ACM Communications in Computer Algebra 2 European Actuarial Journal 2 Mathematics 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Lithuanian Mathematical Journal 1 Mathematical Notes 1 Mathematics of Computation 1 Theory of Probability and its Applications 1 The Annals of Probability 1 Journal of Combinatorial Theory. Series A 1 Journal of Computer and System Sciences 1 Journal of Optimization Theory and Applications 1 Kybernetika 1 Mathematische Nachrichten 1 Mathematica Scandinavica 1 Mathematica Slovaca 1 Mathematika 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Insurance Mathematics & Economics 1 Probability Theory and Related Fields 1 Constructive Approximation 1 Journal of Theoretical Probability 1 Differential Geometry and its Applications 1 Journal of Global Optimization 1 Aequationes Mathematicae 1 European Journal of Operational Research 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Indagationes Mathematicae. New Series 1 Cybernetics and Systems Analysis 1 Documenta Mathematica 1 The Ramanujan Journal 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Annals of Combinatorics 1 Fractional Calculus & Applied Analysis 1 Discrete Dynamics in Nature and Society 1 Acta Mathematica Sinica. English Series 1 Methodology and Computing in Applied Probability 1 Applied Stochastic Models in Business and Industry 1 Foundations of Computational Mathematics 1 Journal of Systems Science and Complexity 1 Decisions in Economics and Finance 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Review of Derivatives Research 1 Boundary Value Problems 1 Applications and Applied Mathematics 1 Mathematics and Financial Economics 1 Logical Methods in Computer Science 1 Algebra & Number Theory 1 Applicable Analysis and Discrete Mathematics 1 Dependence Modeling 1 Journal of Statistical Distributions and Applications 1 Research in Number Theory 1 Proceedings of the American Mathematical Society. Series B 1 Journal of Combinatorial Algebra
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### Cited in 43 Fields

 119 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 87 Probability theory and stochastic processes (60-XX) 36 Special functions (33-XX) 20 Number theory (11-XX) 17 Computer science (68-XX) 13 Combinatorics (05-XX) 13 Numerical analysis (65-XX) 12 Partial differential equations (35-XX) 12 Approximations and expansions (41-XX) 10 Real functions (26-XX) 10 Ordinary differential equations (34-XX) 9 Systems theory; control (93-XX) 8 Operations research, mathematical programming (90-XX) 7 Functions of a complex variable (30-XX) 7 Statistics (62-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 3 Mathematical logic and foundations (03-XX) 3 Commutative algebra (13-XX) 3 Difference and functional equations (39-XX) 3 Sequences, series, summability (40-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral transforms, operational calculus (44-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Field theory and polynomials (12-XX) 2 Potential theory (31-XX) 2 Operator theory (47-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX)