Bauer, B., & Gerhold, S. (2024). The Fan-Taussky-Todd inequalities and the Lumer-Phillips theorem. Journal of Inequalities and Special Functions, 15(1), 23–30. https://doi.org/10.34726/8220 ( reposiTUm)
Gerhold, S. (2023). Small ball probabilities and large deviations for grey Brownian motion. Electronic Communications in Probability, 28, 1–8. https://doi.org/10.1214/23-ECP555 ( reposiTUm)
Gerhold, S., & Thomas, S. (2023). A converse to the neo-classical inequality with an application to the Mittag-Leffler function. Monatshefte Für Mathematik, 200(3), 627–645. https://doi.org/10.1007/s00605-022-01817-8 ( reposiTUm)
Gerhold, S., Hubalek, F., & Paris, R. B. (2022). The running maximum of the Cox-Ingersoll-Ross process with some properties of the Kummer function. Journal of Inequalities and Special Functions, 13(2), 1–18. https://doi.org/10.54379/jiasf-2022-2-1 ( reposiTUm)
Tomovski, Ž., & Gerhold, S. (2022). Mathieu-Fibonacci series. Journal of Integer Sequences, 25(6), Article 22.6.3. ( reposiTUm)
Tomovski, Ž., Gerhold, S., Bansal, D., & Soni, A. (2022). Geometric Properties of Some Generalized Mathieu Power Series inside the Unit Disk. Axioms, 11(10), Article 568. https://doi.org/10.3390/axioms11100568 ( reposiTUm)
Tomovski, Ž., Metzler, R., & Gerhold, S. (2022). Fractional characteristic functions, and a fractional calculus approach for moments of random variables. Fractional Calculus and Applied Analysis, 25(4), 1307–1323. https://doi.org/10.1007/s13540-022-00047-x ( reposiTUm)
Forde, M., Fukasawa, M., Gerhold, S., & Smith, B. (2022). The Riemann-Liouville field and its GMC as 𝐻 → 0, and skew flattening for the rough Bergomi model. Statistics and Probability Letters, 181, Article 109265. https://doi.org/10.1016/j.spl.2021.109265 ( reposiTUm)
Gerhold, S. (2021). A note on large deviations in insurance risk. Applications and Applied Mathematics: An International Journal (A A M), 16(2), 867–880. http://hdl.handle.net/20.500.12708/138591 ( reposiTUm)
Gerhold, S., Gerstenecker, C., & Gulisashvili, A. (2021). Large deviations for fractional volatility models with non-Gaussian volatility driver. Stochastic Processes and Their Applications, 142, 580–600. https://doi.org/10.1016/j.spa.2021.09.010 ( reposiTUm)
Gerhold, S., Jacquier, A., Pakkanen, M., Stone, H., & Wagenhofer, T. (2021). Pathwise large deviations for the rough Bergomi model: Corrigendum. Journal of Applied Probability, 58(3), 849–850. https://doi.org/10.1017/jpr.2020.109 ( reposiTUm)
Forde, M., Gerhold, S., & Smith, B. (2020). Small-time, large-time and H→0 asymptotics for the rough Heston model. Mathematical Finance, 31(1), 203–241. https://doi.org/10.1111/mafi.12290 ( reposiTUm)
Gerhold, S., & Gerstenecker, C. (2020). Large deviations related to the law of the iterated logarithm for Ito diffusions. Electronic Communications in Probability, 25(none). https://doi.org/10.1214/20-ecp297 ( reposiTUm)
Gerhold, S., & Tomovski, Ž. (2019). Asymptotic expansion of Mathieu power series and trigonometric Mathieu series. Journal of Mathematical Analysis and Applications, 479(2), 1882–1892. https://doi.org/10.1016/j.jmaa.2019.07.029 ( reposiTUm)
Gerhold, S., & Gülüm, I. C. (2019). Peacocks nearby: Approximating sequences of measures. Stochastic Processes and Their Applications, 129(7), 2406–2436. https://doi.org/10.1016/j.spa.2018.07.007 ( reposiTUm)
Friz, P., Gerhold, S., & Pinter, A. (2017). Option Pricing in the Moderate Deviations Regime. Mathematical Finance, 28(3), 962–988. https://doi.org/10.1111/mafi.12156 ( reposiTUm)
Gerhold, S., Gülüm, I. C., & Pinter, A. (2016). Small-maturity asymptotics for the at-the-money implied volatility slope in Lévy models. Applied Mathematical Finance, 23(2), 135–157. https://doi.org/10.1080/1350486x.2016.1197041 ( reposiTUm)
Gerhold, S., Kleinert, M., Porkert, P., & Shkolnikov, M. (2015). Small time central limit theorems for semimartingales with applications. Stochastics: An International Journal of Probability and Stochastic Processes, 87(5), 723–746. https://doi.org/10.1080/17442508.2014.1000326 ( reposiTUm)
Gerhold, S., Morgenbesser, J. F., & Zrunek, A. (2015). Refined wing asymptotics for the Merton and Kou jump diffusion models. Banach Center Publications, 104, 85–94. https://doi.org/10.4064/bc104-0-4 ( reposiTUm)
Gerhold, S., Guasoni, P., Muhle-Karbe, J., & Schachermayer, W. (2014). Transaction Costs, Trading Volume, and the Liquidity Premium. Finance and Stochastics, 18(1), 1–37. https://doi.org/10.1007/s00780-013-0210-y ( reposiTUm)
Drmota, M., & Gerhold, S. (2014). Disproof of a conjecture by Rademacher on partial fractions. Proceedings of the American Mathematical Society: Series B, 1(11), 121–134. https://doi.org/10.1090/s2330-1511-2014-00014-6 ( reposiTUm)
Gerhold, S., Muhle-Karbe, J., & Schachermayer, W. (2013). The dual optimizer for the growth-optimal portfolio under transaction costs. Finance and Stochastics, 17(2), 325–354. https://doi.org/10.1007/s00780-011-0165-9 ( reposiTUm)
ALTAY, S., GERHOLD, S., HAIDINGER, R., & HIRHAGER, K. (2013). Digital Double Barrier Options: Several Barrier Periods and Structure Floors. International Journal of Theoretical and Applied Finance, 16(08), 1350044. https://doi.org/10.1142/s0219024913500441 ( reposiTUm)
Gerhold, S., Muhle-Karbe, J., & Schachermayer, W. (2012). Asymptotics and duality for the Davis and Norman problem. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 84(5–6), 625–641. https://doi.org/10.1080/17442508.2011.619699 ( reposiTUm)
Gerhold, S. (2011). The Longstaff-Schwartz Algorithm for Lévy Models: Results on Fast and Slow Convergence. Annals of Applied Probability, 21(2). https://doi.org/10.1214/10-aap704 ( reposiTUm)
Gerhold, S. (2011). The Hartman-Watson distribution revisited: asymptotics for pricing Asian options. Journal of Applied Probability, 48(3), 892–899. https://doi.org/10.1239/jap/1316796924 ( reposiTUm)
Gerhold, S., Schmock, U., & Warnung, R. (2010). A Generalization of the Panjer Recursion and Numerically Stable Risk Aggregation. Finance and Stochastics, 14(1), 81–128. https://doi.org/10.1007/s00780-009-0104-1 ( reposiTUm)
Gerhold, S. (2010). Unimodality of Two Distributions Related to the Negative Binomial Distribution. Journal of Statistical Theory and Applications, 9(1), 1–7. http://hdl.handle.net/20.500.12708/167079 ( reposiTUm)
Gerhold, S. (2009). Asymptotic Analysis of Some Discrete Distributions by the Saddle Point Method. Communications in Statistics - Theory and Methods, 38(2), 262–271. https://doi.org/10.1080/03610920802192489 ( reposiTUm)
Gerhold, S., & Warnung, R. (2009). Finding efficient recursions for risk aggregation by computer algebra. Journal of Computational and Applied Mathematics, 223(1), 499–507. https://doi.org/10.1016/j.cam.2008.01.025 ( reposiTUm)
Bell, J. P., Gerhold, S., Klazar, M., & Luca, F. (2008). Non-Holonomicity of Sequences defined via Elementary Functions. Annals of Combinatorics, 12(1), 1–16. https://doi.org/10.1007/s00026-008-0333-6 ( reposiTUm)
Gerhold, S., Glebsky, L., Schneider, C., Weiss, H., & Zimmermann, B. (2008). Computing the complexity for Schelling segregation models. Communications in Nonlinear Science and Numerical Simulation, 13(10), 2236–2245. https://doi.org/10.1016/j.cnsns.2007.04.023 ( reposiTUm)
Hubalek, F., & Gerhold, S. (2024). The effect of policy cancellation on the risk of an insurance portfolio. In “Advances in Actuarial Science and Finance” : A Conference in Honour of Prof. Takis Papaioannou (pp. 3–3). ( reposiTUm)
Gerhold, S. (2023). Consistency of option prices under bid-ask spreads. In G. Tsaklidis, D. Kugiumtzis, & R. Lykou (Eds.), Book of Abstracts : 10th International Workshop on Applied Probability : IWAP 2023 (pp. 60–60). ( reposiTUm)
Beiträge in Büchern
Gerhold, S., Jacquier, A., & Rosenbaum, M. (2023). Rough Heston. In C. Bayer, P. K. Friz, M. Fukasawa, J. Gatheral, A. Jacquier, & M. Rosenbaum (Eds.), Rough volatility (pp. 83–101). SIAM. https://doi.org/10.1137/1.9781611977783.ch4 ( reposiTUm)
Gerhold, S., & Pinter, A. (2020). Difference Equation Theory Meets Mathematical Finance. In V. Pillwein & C. Schneider (Eds.), Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra (pp. 197–213). Springer Nature Switzerland AG 2020. https://doi.org/10.1007/978-3-030-44559-1_11 ( reposiTUm)
Friz, P., & Gerhold, S. (2015). Extrapolation Analytics for Dupire’s Local Volatility. In P. Friz, J. Gatheral, A. Gulisashvili, A. Jacquier, & J. Teichmann (Eds.), Springer Proceedings in Mathematics & Statistics (pp. 273–286). Springer. https://doi.org/10.1007/978-3-319-11605-1_10 ( reposiTUm)
Gerhold, S., Kauers, M., Koutschan, C., Paule, P., Schneider, C., & Zimmermann, B. (2013). Computer-Assisted Proofs of Some Identities for Bessel Functions of Fractional Order. In Texts & Monographs in Symbolic Computation (pp. 75–96). Springer Verlag. https://doi.org/10.1007/978-3-7091-1616-6_3 ( reposiTUm)
Benoit, A., Chyzak, F., Darrasse, A., Gerhold, S., Mezzarobba, M., & Salvy, B. (2010). The Dynamic Dictionary of Mathematical Functions (DDMF). In Mathematical Software – ICMS 2010 (pp. 35–41). Springer. https://doi.org/10.1007/978-3-642-15582-6_7 ( reposiTUm)
Gerhold, S., & Hubalek, F. (2024, August 16). The effect of policy cancellation on the risk of an insurance portfolio [Conference Presentation]. Scandinavian Actuarial Conference 2024, Copenhagen, Denmark. ( reposiTUm)
Gerhold, S., Gülüm, I. C., & Hubalek, F. (2024, October 21). Some musings on Strassen’s theorem: From bid-ask spreads to life insurance [Keynote Presentation]. Stochastics in Mathematical Finance and Physics Conference, Tunis, Tunisia. ( reposiTUm)
Wiedermann, K., Friesen, M., & Gerhold, S. (2024, July 12). A small-time central limit theorem for stochastic Volterra integral equations and its implications on the Markov property [Conference Presentation]. 12th Bachelier World Congress, Rio de Janeiro, Brazil. ( reposiTUm)
Gerhold, S., Wiedermann, K., & Bauer, B. (2024, April 17). On the non-Markov property: Gaussian processes and beyond [Presentation]. Torino seminar series in Stochastics and Mathematical Statistics, Turin, Italy. http://hdl.handle.net/20.500.12708/208306 ( reposiTUm)
Wiedermann, K., Friesen, M., & Gerhold, S. (2024, October 24). Small-time central limit theorems for stochastic Volterra integral equations and their implications on the Markov property [Conference Presentation]. Stochastics in Mathematical Finance and Physics Conference, Hammamet, Tunisia. http://hdl.handle.net/20.500.12708/209502 ( reposiTUm)
Gerhold, S., & Wiedermann, K. (2023, March 7). A CLT for Solutions to Stochastic Volterra Integral Equations [Conference Presentation]. 16th German Probability and Statistics Days GPSD 2023, Essen, Germany. http://hdl.handle.net/20.500.12708/191889 ( reposiTUm)
Gerhold, S. (2023, November 28). Fractional models in financial option pricing [Conference Presentation]. Fractional Differential Equations, Applications and Complex Networks 2023, Snellius, Netherlands (the). ( reposiTUm)
Gerhold, S. (2023, March 7). Asymptotic pricing of VIX options under rough volatility [Conference Presentation]. 16th German Probability and Statistics Days 2023, Essen, Germany. ( reposiTUm)
Gerhold, S. (2023, May 4). Die Mathematik der Finanzmärkte [Presentation]. TUforMath 2023, Wien, Austria. ( reposiTUm)
Gerhold, S. (2023, May 22). Fractional models from econophysics [Conference Presentation]. Volatility is rough. Now what? 2023, Isle of Skye, United Kingdom of Great Britain and Northern Ireland (the). ( reposiTUm)
Gerhold, S. (2021). Asymptotic pricing of VIX options under rough volatility. Vienna Seminar in Mathematical Finance and Probability, University of Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/123374 ( reposiTUm)
Gerhold, S. (2019). Small-time and large-time smile behaviour for the rough Heston model. International Conference on Computational Finance 2019 (ICCF2019), Fundación Pedro Barrié de la Maza, Coruña, Spain. http://hdl.handle.net/20.500.12708/122789 ( reposiTUm)
Gerhold, S. (2019). Dynamic trading under integer constraints. Vienna Seminar in Mathematical Finance and Probability, TU Wien, University of Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/123004 ( reposiTUm)
Gerhold, S. (2019). Asymptotic approximations of option prices in rough volatility models. AAP Editorial Board Meeting, Universität Nizza Sophia-Antipolis, France. http://hdl.handle.net/20.500.12708/122996 ( reposiTUm)
Gerhold, S. (2019). Dynamic trading under integer constraints. Research Seminar “Stochastische Analysis und Stochastik der Finanzmärkte,” TU Berlin, Berlin, Germany. http://hdl.handle.net/20.500.12708/122999 ( reposiTUm)
Gerhold, S. (2019). Small-time and large-time smile behaviour for the rough Heston model. 9th General Advanced Mathematical Methods in Finance (AMaMeF) Conference, Sorbonne Université, Paris, France. http://hdl.handle.net/20.500.12708/122771 ( reposiTUm)
Gerhold, S. (2018). Recollections of my time in Peter’s group. Combinatorics, Special Functions and Computer Algebra - A workshop at the occasion of Peter Paule’s 60th birthday (Paule60), Research Institute for Symbolic Computation (RISC), Hagenberg, Austria, Austria. http://hdl.handle.net/20.500.12708/122530 ( reposiTUm)
Gerhold, S. (2018). Dynamic trading under integer constraints. Finance and Stochastics Seminar, London, United Kingdom of Great Britain and Northern Ireland (the). http://hdl.handle.net/20.500.12708/122523 ( reposiTUm)
Gerhold, S. (2017). Consistency of option prices under bid-ask spreads. Oberwolfach Workshop “Mathematics of Quantitative Finance,” Oberwolfach, Germany. http://hdl.handle.net/20.500.12708/122164 ( reposiTUm)
Gerhold, S. (2017). Consistency of option prices under bid-ask spreads. Workshop in Wahrscheinlichkeitstheorie, Statistik und Finanzmathematik, TU Dresden, Germany. http://hdl.handle.net/20.500.12708/122160 ( reposiTUm)
Gerhold, S. (2016). Option Pricing in the Moderate Deviations Regime. BFS 2016 - 9th World Congress of the Bachelier Finance Society, New York, U.S.A., Non-EU. http://hdl.handle.net/20.500.12708/121745 ( reposiTUm)
Gerhold, S. (2016). Asymptotic approximations of implied and local volatility. Candidate Lecture, Faculty of Mathematics, University of Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/121734 ( reposiTUm)
Gerhold, S. (2016). Option Pricing in the Moderate Deviations Regime. CSASC - Joint Meeting of the Czech, Slovenian, Austrian, Slovak and Catalan mathematical societies, Barcelona, Spain. http://hdl.handle.net/20.500.12708/121765 ( reposiTUm)
Gerhold, S. (2016). Trying to find the characteristic function of Rosenbaum’s fractional Heston model. Meeting “Rough Volatility,” London, United Kingdom of Great Britain and Northern Ireland (the). http://hdl.handle.net/20.500.12708/121768 ( reposiTUm)
Gerhold, S. (2015). Adaptive strategies in the Merton problem. Research Seminar of the Mathematical Finance Group of University of Vienna, Wolkersdorf, Austria, Austria. http://hdl.handle.net/20.500.12708/121274 ( reposiTUm)
Gerhold, S. (2015). Utility maximization and symbolic computation. 13th International Symposium on Orthogonal Polynomials, Special Functions & Applications, ational Institute of Standards and Technology, Gaithersburg, Maryland, United States of America (the). http://hdl.handle.net/20.500.12708/121289 ( reposiTUm)
Gerhold, S. (2014). The Small-Maturity Implied Volatility Slope for Lévy Models. SIAM Conference on Financial Mathematics and Engineering, Chicago, Illinois, USA, Non-EU. http://hdl.handle.net/20.500.12708/120952 ( reposiTUm)
Gerhold, S. (2014). Disproof of a conjecture by Rademacher on partial fractions. Seminar Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, Austria. http://hdl.handle.net/20.500.12708/120981 ( reposiTUm)
Gerhold, S. (2014). Disproof of a conjecture by Rademacher on partial fractions. Mathematisches Kolloquium der Universität Wien, Universität Wien, Austria. http://hdl.handle.net/20.500.12708/120976 ( reposiTUm)
Gerhold, S. (2014). The Small Maturity Implied Volatility Slope for Lévy Models. 8th World Congress of the Bachelier Finance Society (BFS 2014), Brussels, Belgium, EU. http://hdl.handle.net/20.500.12708/120967 ( reposiTUm)
Gerhold, S. (2014). Small time central limit theorems for semimartingales and the implied volatility skew. 11th International Vilnius Conference on Probability Theory and Mathematical Statistics, Vilnius, Lithuania, EU. http://hdl.handle.net/20.500.12708/120966 ( reposiTUm)
Gerhold, S. (2013). Local volatility models: approximation and regularization. 18th ÖMG Congress and Annual DMV Meeting, Universität Innsbruck, Austria. http://hdl.handle.net/20.500.12708/120655 ( reposiTUm)
Gerhold, S. (2013). Local volatility models: approximation and regularization. International Conference Advanced Finance and Stochastics, teklov Mathematical Institute, Moscow, Russia, Non-EU. http://hdl.handle.net/20.500.12708/120656 ( reposiTUm)
Gerhold, S. (2013). Local Volatility Models: Approximation and Regularization. PRisMa Day - Workshop on Portfolio Risk Management, Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/120651 ( reposiTUm)
Gerhold, S. (2013). Small time central limit theorems for semimartingales with applications. German-Polish Joint Conference on Probability Theory and Mathematical Statistics, University of Warsaw, Warsaw, Poland, EU. http://hdl.handle.net/20.500.12708/120684 ( reposiTUm)
Gerhold, S. (2013). Local volatility models: Approximation and regularization. Advances in Mathematics of Finance - 6th General AMaMeF and Banach Center Conference, University of Warsaw, Warsaw, Poland, EU. http://hdl.handle.net/20.500.12708/120683 ( reposiTUm)
Gerhold, S. (2013). Some traces of discrete mathematics in mathematical finance. Seminar Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, Austria. http://hdl.handle.net/20.500.12708/120700 ( reposiTUm)
Gerhold, S. (2013). Local volatility asymptotics and small-time central limit theorems. Workshop on Large deviations and asymptotic methods in finance, Imperial College London, UK, EU. http://hdl.handle.net/20.500.12708/120692 ( reposiTUm)
Gerhold, S. (2012). Portfolio optimization under transaction costs. 12th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear Dynamics, TU Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/120246 ( reposiTUm)
Gerhold, S. (2012). Don’t stay local - extrapolation analytics for Dupire’s local volatility. 7th World Congress of the Bachelier Finance Society, Sydney, Australia, Non-EU. http://hdl.handle.net/20.500.12708/120260 ( reposiTUm)
Gerhold, S. (2012). Portfolio optimization under transaction costs. Berufungsvorträge für Professur “Stochastische Methoden in den Wirtschaftswissenschaften,” TU Wien, Austria, Austria. http://hdl.handle.net/20.500.12708/120263 ( reposiTUm)
Gerhold, S. (2012). Transaction Costs, Trading Volume, and the Liquidity Premium. 10th German Probability and Statistics Days 2012 - Stochastik-Tage Mainz, University of Mainz, Mainz, Germany, EU. http://hdl.handle.net/20.500.12708/120266 ( reposiTUm)
Gerhold, S. (2011). Refined Volatility Expansion in the Heston Model. ICIAM 2011 - 7th International Congress on Industrial and Applied Mathematics, Vancouver, Non-EU. http://hdl.handle.net/20.500.12708/119897 ( reposiTUm)
Gerhold, S. (2011). Transaction Costs, Trading Volume, and the Liquidity Premium. PRisMa Day - Workshop on Portfolio Risk Management, Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/119898 ( reposiTUm)
Gerhold, S. (2010). Refined volatility expansion in the Heston model. Conference on Analysis, Stochastics, and Applications (AnStAp), Vienna University, Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/119644 ( reposiTUm)
Gerhold, S. (2010). On Refined Volatility Smile Expansion In The Heston Model. World Congress of the Bachelier Finance Society, Tokyo, Japan, Non-EU. http://hdl.handle.net/20.500.12708/119399 ( reposiTUm)
Gerhold, S. (2009). Lindelöf integral representations and asymptotic analysis of a certain power series with closed-form coefficients. Institut für Diskrete Mathematik und Geometrie, Wien, Austria, Austria. http://hdl.handle.net/20.500.12708/119154 ( reposiTUm)
Gerhold, S. (2008). Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for American Option Pricing. PRisMa Day - Workshop on Portfolio Risk Management, Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/118880 ( reposiTUm)
Gerhold, S. (2008). Lévy-Sheffer Systems and the Longstaff-Schwartz Algorithm for American Option Pricing. Conference on Numerical Methods for American and Bermudan Options, Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/118881 ( reposiTUm)
Gerhold, S. (2007). The Sign Structure of Linear Recurrence Sequences. Conference on Progress on Difference Equations, University Laufen, Germany, EU. http://hdl.handle.net/20.500.12708/118343 ( reposiTUm)
Gerhold, S. (2006). An Implementation of the LIBOR Market Model for Pricing Exotic Constant Maturity Swaps. PRisMa Day 2006 - One-Day Workshop on Portfolio Risk Management, TU Vienna, Austria, Austria. http://hdl.handle.net/20.500.12708/117950 ( reposiTUm)
Gerhold, S. (2006). Special Functions: Applications of Computer Algebra in Stochastics. Radon Institute der österr. Akademie der Wissenschaften, Linz, Linz, Österreich, Austria. http://hdl.handle.net/20.500.12708/117987 ( reposiTUm)
Gerhold, S. (2010). Special functions : from Lindelöf integrals to volatility smiles [Professorial Dissertation, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/159541 ( reposiTUm)