Edit Profile Gerhold, Stefan Compute Distance To: Compute Author ID: gerhold.stefan Published as: Gerhold, S.; Gerhold, Stefan External Links: MGP · Wikidata Documents Indexed: 47 Publications since 2004 Reviewing Activity: 7 Reviews all top 5 Co-Authors 14 single-authored 4 Friz, Peter Karl 4 Kauers, Manuel 4 Pinter, Arpad 3 Gülüm, Ismail Cetin 3 Muhle-Karbe, Johannes 3 Salvy, Bruno 3 Schachermayer, Walter 2 Bell, Jason P. 2 Flajolet, Philippe 2 Gerstenecker, Christoph 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 Glebsky, Lev Yu. 1 Guasoni, Paolo 1 Gulisashvili, Archil 1 Haidinger, Rainer 1 Hirhager, Karin 1 Hubalek, Friedrich 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 Paule, Peter 1 Porkert, Piet 1 Schmock, Uwe 1 Shkolnikov, Mykhaylo 1 Sturm, Stephan 1 Weiss, Howard 1 Yor, Marc 1 Zeiner, Martin 1 Zrunek, Axel all top 5 Serials 4 Finance and Stochastics 3 The Electronic Journal of Combinatorics 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 Applied Probability 1 Journal of Computational and Applied Mathematics 1 Mathematica Scandinavica 1 Statistics & Probability Letters 1 The Annals of Applied Probability 1 Communications in Statistics. Theory and Methods 1 Stochastic Processes and their Applications 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 all top 5 Fields 22 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 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 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) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 35 Publications have been cited 236 times in 176 Documents Cited by ▼ Year ▼ Transaction costs, trading volume, and the liquidity premium. Zbl 1305.91218Gerhold, Stefan; Guasoni, Paolo; Muhle-Karbe, Johannes; Schachermayer, Walter 31 2014 On refined volatility smile expansion in the Heston model. Zbl 1267.91068Friz, Peter; Gerhold, Stefan; Gulisashvili, Archil; Sturm, Stephan 21 2011 The dual optimizer for the growth-optimal portfolio under transaction costs. Zbl 1319.91142Gerhold, S.; Muhle-Karbe, J.; Schachermayer, W. 19 2013 Asymptotics and duality for the Davis and Norman problem. Zbl 1276.91093Gerhold, Stefan; Muhle-Karbe, Johannes; Schachermayer, Walter 16 2012 A procedure for proving special function inequalities involving a discrete parameter. Zbl 1360.68933Gerhold, Stefan; Kauers, Manuel 14 2005 Asymptotics for a variant of the Mittag-Leffler function. Zbl 1257.33050Gerhold, Stefan 12 2012 On the non-holonomic character of logarithms, powers, and the \(n\)th prime function. Zbl 1076.05004Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno 12 2005 How to make Dupire’s local volatility work with jumps. Zbl 1402.91776Friz, Peter K.; Gerhold, Stefan; Yor, Marc 10 2014 On Turán’s inequality for Legendre polynomials. Zbl 1155.26012Alzer, Horst; Gerhold, Stefan; Kauers, Manuel; Lupaş, Alexandru 9 2007 The longstaff-Schwartz algorithm for Lévy models: results on fast and slow convergence. Zbl 1219.62161Gerhold, Stefan 8 2011 On the positivity set of a linear recurrence sequence. Zbl 1139.11010Bell, Jason P.; Gerhold, Stefan 8 2007 Option pricing in the moderate deviations regime. Zbl 1411.91554Friz, Peter; Gerhold, Stefan; Pinter, Arpad 6 2018 Lindelöf representations and (non-)holonomic sequences. Zbl 1222.05005Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno 6 2010 Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian 6 2008 Disproof of a conjecture by Rademacher on partial fractions. Zbl 1339.11087Drmota, Michael; Gerhold, Stefan 5 2014 A computer proof of Turán’s inequality. Zbl 1132.26336Gerhold, Stefan; Kauers, Manuel 5 2006 Moment explosions in the rough Heston model. Zbl 1432.91123Gerhold, Stefan; Gerstenecker, Christoph; Pinter, Arpad 4 2019 Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models. Zbl 1396.91731Gerhold, Stefan; Gülüm, I. Cetin; Pinter, Arpad 4 2016 Extrapolation analytics for Dupire’s local volatility. Zbl 1418.91511Friz, Peter; Gerhold, Stefan 4 2015 A generalization of Panjer’s recursion and numerically stable risk aggregation. Zbl 1224.91060Gerhold, Stefan; Schmock, Uwe; Warnung, Richard 4 2010 The dynamic dictionary of mathematical functions (DDMF). Zbl 1295.65022Benoit, Alexandre; Chyzak, Frédéric; Darrasse, Alexis; Gerhold, Stefan; Mezzarobba, Marc; Salvy, Bruno 3 2010 Asymptotic estimates for some number-theoretic power series. Zbl 1206.11116Gerhold, Stefan 3 2010 Point lattices and oscillating recurrence sequences. Zbl 1204.11024Gerhold, Stefan 3 2005 On some non-holonomic sequences. Zbl 1063.11007Gerhold, Stefan 3 2004 Asymptotic expansion of Mathieu power series and trigonometric Mathieu series. Zbl 1450.30006Gerhold, Stefan; Tomovski, Živorad 2 2019 Small time central limit theorems for semimartingales with applications. Zbl 1337.60020Gerhold, Stefan; Kleinert, Max; Porkert, Piet; Shkolnikov, Mykhaylo 2 2015 Refined wing asymptotics for the Merton and Kou jump diffusion models. Zbl 1312.91087Gerhold, Stefan; Morgenbesser, Johannes F.; Zrunek, Axel 2 2015 Can there be an explicit formula for implied volatility? Zbl 1315.91062Gerhold, Stefan 2 2013 Counting finite languages by total word length. Zbl 1234.05024Gerhold, Stefan 2 2011 The Hartman-Watson distribution revisited: asymptotics for pricing Asian options. Zbl 1279.62041Gerhold, Stefan 2 2011 Moment explosion in the LIBOR market model. Zbl 1208.91152Gerhold, Stefan 2 2011 Finding efficient recursions for risk aggregation by computer algebra. Zbl 1153.91592Gerhold, Stefan; Warnung, Richard 2 2009 Computing the complexity for Schelling segregation models. Zbl 1221.37185Gerhold, Stefan; Glebsky, Lev; Schneider, Carsten; Weiss, Howard; Zimmermann, Burkhard 2 2008 Small-maturity digital options in Lévy models: an analytic approach. Zbl 1321.60093Gerhold, Stefan 1 2015 Convergence properties of Kemp’s \(q\)-binomial distribution. Zbl 1213.60045Gerhold, Stefan; Zeiner, Martin 1 2010 Moment explosions in the rough Heston model. Zbl 1432.91123Gerhold, Stefan; Gerstenecker, Christoph; Pinter, Arpad 4 2019 Asymptotic expansion of Mathieu power series and trigonometric Mathieu series. Zbl 1450.30006Gerhold, Stefan; Tomovski, Živorad 2 2019 Option pricing in the moderate deviations regime. Zbl 1411.91554Friz, Peter; Gerhold, Stefan; Pinter, Arpad 6 2018 Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models. Zbl 1396.91731Gerhold, Stefan; Gülüm, I. Cetin; Pinter, Arpad 4 2016 Extrapolation analytics for Dupire’s local volatility. Zbl 1418.91511Friz, Peter; Gerhold, Stefan 4 2015 Small time central limit theorems for semimartingales with applications. Zbl 1337.60020Gerhold, Stefan; Kleinert, Max; Porkert, Piet; Shkolnikov, Mykhaylo 2 2015 Refined wing asymptotics for the Merton and Kou jump diffusion models. Zbl 1312.91087Gerhold, Stefan; Morgenbesser, Johannes F.; Zrunek, Axel 2 2015 Small-maturity digital options in Lévy models: an analytic approach. Zbl 1321.60093Gerhold, Stefan 1 2015 Transaction costs, trading volume, and the liquidity premium. Zbl 1305.91218Gerhold, Stefan; Guasoni, Paolo; Muhle-Karbe, Johannes; Schachermayer, Walter 31 2014 How to make Dupire’s local volatility work with jumps. Zbl 1402.91776Friz, Peter K.; Gerhold, Stefan; Yor, Marc 10 2014 Disproof of a conjecture by Rademacher on partial fractions. Zbl 1339.11087Drmota, Michael; Gerhold, Stefan 5 2014 The dual optimizer for the growth-optimal portfolio under transaction costs. Zbl 1319.91142Gerhold, S.; Muhle-Karbe, J.; Schachermayer, W. 19 2013 Can there be an explicit formula for implied volatility? Zbl 1315.91062Gerhold, Stefan 2 2013 Asymptotics and duality for the Davis and Norman problem. Zbl 1276.91093Gerhold, Stefan; Muhle-Karbe, Johannes; Schachermayer, Walter 16 2012 Asymptotics for a variant of the Mittag-Leffler function. Zbl 1257.33050Gerhold, Stefan 12 2012 On refined volatility smile expansion in the Heston model. Zbl 1267.91068Friz, Peter; Gerhold, Stefan; Gulisashvili, Archil; Sturm, Stephan 21 2011 The longstaff-Schwartz algorithm for Lévy models: results on fast and slow convergence. Zbl 1219.62161Gerhold, Stefan 8 2011 Counting finite languages by total word length. Zbl 1234.05024Gerhold, Stefan 2 2011 The Hartman-Watson distribution revisited: asymptotics for pricing Asian options. Zbl 1279.62041Gerhold, Stefan 2 2011 Moment explosion in the LIBOR market model. Zbl 1208.91152Gerhold, Stefan 2 2011 Lindelöf representations and (non-)holonomic sequences. Zbl 1222.05005Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno 6 2010 A generalization of Panjer’s recursion and numerically stable risk aggregation. Zbl 1224.91060Gerhold, Stefan; Schmock, Uwe; Warnung, Richard 4 2010 The dynamic dictionary of mathematical functions (DDMF). Zbl 1295.65022Benoit, Alexandre; Chyzak, Frédéric; Darrasse, Alexis; Gerhold, Stefan; Mezzarobba, Marc; Salvy, Bruno 3 2010 Asymptotic estimates for some number-theoretic power series. Zbl 1206.11116Gerhold, Stefan 3 2010 Convergence properties of Kemp’s \(q\)-binomial distribution. Zbl 1213.60045Gerhold, Stefan; Zeiner, Martin 1 2010 Finding efficient recursions for risk aggregation by computer algebra. Zbl 1153.91592Gerhold, Stefan; Warnung, Richard 2 2009 Non-holonomicity of sequences defined via elementary functions. Zbl 1189.11007Bell, Jason P.; Gerhold, Stefan; Klazar, Martin; Luca, Florian 6 2008 Computing the complexity for Schelling segregation models. Zbl 1221.37185Gerhold, Stefan; Glebsky, Lev; Schneider, Carsten; Weiss, Howard; Zimmermann, Burkhard 2 2008 On Turán’s inequality for Legendre polynomials. Zbl 1155.26012Alzer, Horst; Gerhold, Stefan; Kauers, Manuel; Lupaş, Alexandru 9 2007 On the positivity set of a linear recurrence sequence. Zbl 1139.11010Bell, Jason P.; Gerhold, Stefan 8 2007 A computer proof of Turán’s inequality. Zbl 1132.26336Gerhold, Stefan; Kauers, Manuel 5 2006 A procedure for proving special function inequalities involving a discrete parameter. Zbl 1360.68933Gerhold, Stefan; Kauers, Manuel 14 2005 On the non-holonomic character of logarithms, powers, and the \(n\)th prime function. Zbl 1076.05004Flajolet, Philippe; Gerhold, Stefan; Salvy, Bruno 12 2005 Point lattices and oscillating recurrence sequences. Zbl 1204.11024Gerhold, Stefan 3 2005 On some non-holonomic sequences. Zbl 1063.11007Gerhold, Stefan 3 2004 all cited Publications top 5 cited Publications all top 5 Cited by 273 Authors 15 Gerhold, Stefan 11 Jacquier, Antoine 11 Muhle-Karbe, Johannes 8 Kauers, Manuel 7 Friz, Peter Karl 7 Guasoni, Paolo 5 Gulisashvili, Archil 5 Pillwein, Veronika 5 Schachermayer, Walter 4 Baricz, Árpád 4 Lorig, Matthew J. 4 O’Sullivan, Cormac 4 Pagliarani, Stefano 4 Pascucci, Andrea 4 Pinter, Arpad 3 De Marco, Stefano 3 Herdegen, Martin 3 Kallsen, Jan 3 Soner, Halil Mete 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 Bouchard, Bruno 2 Chen, Shaoshi 2 Czichowsky, Christoph 2 Deuschel, Jean-Dominique 2 Dolinsky, Yan 2 Forde, Martin 2 Fukasawa, Masaaki 2 Gatheral, Jim 2 Horvath, Blanka 2 Lin, Yiqing 2 Luca, Florian 2 Martini, Claude 2 Pirjol, Dan 2 Rogosin, Sergei V. 2 Roome, Patrick 2 Salvy, Bruno 2 Sass, Jörn 2 Schneider, Carsten 2 Shi, Fangwei 2 Tomovski, Živorad 2 Violante, S. 2 Weber, Marko Hans 1 Abbas-Turki, Lokman A. 1 Allaj, Erindi 1 Allouche, Jean-Paul Simon 1 Alonso, Ricardo J. 1 Andersen, Lars Nørvang 1 Asmussen, Søren 1 Atkinson, Colin 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 Berg, Christian 1 Berthomieu, Jérémy 1 Bogdan, Krzysztof 1 Bóna, Miklós 1 Bostan, Alin 1 Bruin, Nils 1 Byszewski, Jakub 1 Campi, Luciano 1 Caravenna, Francesco 1 Ceballos, Manuel 1 Cha, Yongjae 1 Chakraborty, Subrata 1 Chau, Huy N. 1 Chen, William Yong-Chuan 1 Choi, Jin Hyuk 1 Conus, Daniel 1 Coons, Michael 1 Corbetta, Jacopo 1 Cordwell, Katherine 1 Cornelissen, Gunther 1 Crepey, Stephane 1 Dastgerdi, Maryam Vahid 1 De Olivera, Federico 1 Desmettre, Sascha 1 Diallo, Babacar 1 Diao, Xundi 1 Dixit, Atul 1 Dolinskyi, Leonid 1 Dostál, Petr 1 Drmota, Michael 1 Dubickas, Artūras 1 Nguyen Tien Dung 1 Echzell, Hagen 1 El Euch, Omar 1 Ercolani, Nicholas M. ...and 173 more Authors all top 5 Cited in 81 Serials 16 Finance and Stochastics 13 SIAM Journal on Financial Mathematics 9 Mathematical Finance 9 International Journal of Theoretical and Applied Finance 6 Journal of Symbolic Computation 6 Quantitative Finance 4 Advances in Applied Mathematics 4 Stochastics 3 Journal of Number Theory 3 SIAM Journal on Control and Optimization 3 The Annals of Applied Probability 3 Stochastic Processes and their Applications 3 Integral Transforms and Special Functions 3 Applied Mathematical Finance 2 Bulletin of the Australian Mathematical Society 2 Communications on Pure and Applied Mathematics 2 Discrete Applied Mathematics 2 Journal of Applied Probability 2 Journal of Computational and Applied Mathematics 2 Proceedings of the American Mathematical Society 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 Discrete Mathematics 1 Israel Journal of Mathematics 1 Journal of Mathematical Analysis and Applications 1 Mathematical Notes 1 Mathematics of Computation 1 Theory of Probability and its Applications 1 The Annals of Probability 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 Journal of Approximation Theory 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 Mathematics of Operations Research 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 Statistics & Probability Letters 1 Probability Theory and Related Fields 1 Constructive Approximation 1 Journal of Theoretical Probability 1 Journal of Global Optimization 1 Aequationes Mathematicae 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Cybernetics and Systems Analysis 1 Documenta Mathematica 1 The Ramanujan Journal 1 Abstract and Applied Analysis 1 Annals of Combinatorics 1 Fractional Calculus & Applied Analysis 1 Discrete Dynamics in Nature and Society 1 Acta Mathematica Sinica. English Series 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 Boundary Value Problems 1 Applications and Applied Mathematics 1 Mathematics and Financial Economics 1 Algebra & Number Theory 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 all top 5 Cited in 38 Fields 96 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 70 Probability theory and stochastic processes (60-XX) 30 Special functions (33-XX) 20 Number theory (11-XX) 16 Computer science (68-XX) 13 Combinatorics (05-XX) 12 Numerical analysis (65-XX) 11 Partial differential equations (35-XX) 11 Approximations and expansions (41-XX) 8 Real functions (26-XX) 8 Ordinary differential equations (34-XX) 8 Systems theory; control (93-XX) 7 Functions of a complex variable (30-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Statistics (62-XX) 6 Operations research, mathematical programming (90-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 Mathematical logic and foundations (03-XX) 2 Field theory and polynomials (12-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 Potential theory (31-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.