Publications
Hans Föllmer — Book and selected articles in stochastic analysis and mathematical finance.
Stochastic Finance — An Introduction in Discrete Time
With Alexander Schied. de Gruyter Studies in Mathematics 27.
Fifth revised and extended edition
With new sections on stop-loss insurance contracts, the Fatou property of law-invariant risk measures, relative entropy, Cover’s universal portfolios, and numerous additional exercises.
Fourth revised and extended edition
With additional background material and a dozen new exercises.
Third revised and extended edition
- now with more than 100 exercises
- new chapter on dynamic risk measures
- new sections on robust utility maximization and on efficient hedging with convex risk measures
Russian edition
Translated by Yuliya Mishura and Georgiy Shevshenko. Russian edition, MCCME, Moscow.
Second revised and extended edition
First edition: ix + 422 pp., July 2002. Second edition page.
Articles
- Entropic Risk Measures on Wiener Space. To appear in: Stochastic Processes and Control with Applications to Finance, Insurance, and Data Science: A Festschrift in Honor of Robert J. Elliott. Eds. Samuel Cohen, Dilip Madan, Tan Kuen Sir, Hailiang Yang, World Scientific (2026).
- Doob Decomposition, Dirichlet Processes, and Entropies on Wiener Space. In: Festschrift in honour of Masatoshi Fukushima’s Beiju, Proceedings in Mathematics and Statistics, Springer (2022).
- Optimal Couplings on Wiener Space and an Extension of Talagrand’s Transport Inequality. In: Stochastic Analysis, Filtering and Stochastic Optimization: A Commemorative Volume to Honor Mark H. Davis’s Contributions and Applications. Eds. George Yin and T. Zariphopoulou, Springer (2022).
- Consistency Properties of Systemic Risk Measures. In: Risk and Stochastics — Ragnar Norberg. Ed. Pauline Barrieu, World Scientific, 23–42 (2019).
- The Axiomatic Approach to Risk Measures for Capital Determination (with Stefan Weber). Annual Review of Financial Economics, Vol. 7, 301–337 (2015).
- Spatial Risk Measures: Local Specification and Boundary Risk (with Claudia Klüppelberg). In: Stochastic Analysis and Applications 2014 — In Honour of Terry Lyons. Eds. D. Crisan, B. Hambly and T. Zariphopoulou, Springer Proceedings in Mathematics & Statistics 100, 307–326 (2014).
- Consistent Risk Measures and a Non-linear Extension of Backwards Martingale Convergence (with Irina Penner). In: Festschrift Masatoshi Fukushima. Eds. Z.-Q. Chen, N. Jacob, M. Takeda, World Scientific, Interdisciplinary Mathematical Sciences, Vol. 17, 183–202 (2015).
- Shifting Martingale Measures and the Birth of a Bubble as a Submartingale (with Francesca Biagini and Sorin Nedelcu). Finance and Stochastics, Vol. 18, No. 2, 297–326 (2014).
- Spatial Risk Measures and their Local Specification: The Locally Law-Invariant Case. Statistics & Risk Modeling Vol. 31, No. 1, 79–101 (2014).
- Probabilistic Aspects of Finance (with Alexander Schied). Bernoulli, Vol. 19, No. 4, 1306–1326 (2013).
- Convex Risk Measures: Basic Facts, Law-invariance and beyond, Asymptotics for Large Portfolios (with Thomas Knispel). Handbook of the Fundamentals of Financial Decision Making, Part II, 507–554. Eds. L. C. MacLean and W. T. Ziemba, World Scientific (2013).
- Convex Capital Requirements for Large Portfolios (with Thomas Knispel). In: Stochastic Analysis and its Applications to Mathematical Finance, Essays in Honour of Jia-an Yan. Eds. T. Zhang and X. Y. Zhou, World Scientific (2012).
- Risk Assessment for Uncertain Cash Flows: Model Ambiguity, Discounting Ambiguity, and the Role of Bubbles (with Beatrice Acciaio and Irina Penner). Finance and Stochastics, Vol. 16, No. 4, 669–709 (2012).
- Entropic Risk Measures: Coherence vs. Convexity, Model Ambiguity, and Robust Large Deviations (with Thomas Knispel). Stochastics and Dynamics, Vol. 11, Nos. 2&3, 333–351 (2011).
- Monetary Valuation of Cash Flows under Knightian Uncertainty (with Irina Penner). Int. J. Theor. Appl. Finance, Vol. 14, No. 1, 1–15 (2011).
- Local Martingales and Filtration Shrinkage (with Ph. Protter). ESAIM Probability and Statistics, Vol. 15 (special volume in honour of Marc Yor), 25–38 (2011).
- Convex and Coherent Risk Measures (with A. Schied). Encyclopedia of Quantitative Finance. Cont, R. (Ed.). John Wiley & Sons, pp. 1200–1204 (2010).
- The Minimal Martingale Measure (with M. Schweizer). Encyclopedia of Quantitative Finance. Cont, R. (Ed.). Wiley & Sons, pp. 1200–1204 (2010).
- Alles richtig und trotzdem falsch? Anmerkungen zur Finanzkrise und zur Finanzmathematik. Mitteilungen der DMV 17, 148–154 (2009).
- Robust Preferences and Robust Portfolio Choice (with A. Schied and S. Weber). Handbook of Numerical Analysis XV, Bensoussan & Zhang (Eds.), Mathematical Modeling and Numerical Methods in Finance, 29–89 (2009).
- Asymptotic Arbitrage and Large Deviations (with W. Schachermayer). Mathematics and Financial Economics 1 (3–4), 213–249 (2008).
- On Kiyosi Itô’s Work and its Impact. Gauss Lecture at the ICM 2006. Proceedings of the International Congress of Mathematicians, Madrid 2006, Vol. I, 109–124. European Mathematical Society Publishing House (2007).
- A Representation of Excessive Functions as Expected Suprema (with T. Knispel). Probability and Mathematical Statistics 26(2), 379–394, Volume in honor of Kazimierz Urbanik (2006).
- Potentials of a Markov Process are Expected Suprema (with T. Knispel). ESAIM Probability and Statistics 11, 89–101. Special Issue in honor of Nicole El Karoui’s 60th birthday (2007).
- Convex Risk Measures and the Dynamics of their Penalty Functions (with I. Penner). Statistics & Decisions 24(1), 61–96 (2006).
- Robust Projections in the Class of Martingale Measures (with A. Gundel). Illinois Journal of Mathematics 50(2), 439–472 (2006).
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Incertitude financière, mesures de risque et préférences robustes.
Actes du colloque « Aspects des mathématiques financières », Académie des Sciences Paris (Ed. M. Yor), Lavoisier (2006).
PDF (FR) · 124 KB PDF (EN) · 9.4 MB
English version: Financial Uncertainty, Risk Measures, and Robust Preferences. In: Aspects of Mathematical Finance (Ed. M. Yor), 3–15, Springer Berlin (2008).
- A Non-linear Riesz Representation in Probabilistic Potential Theory (with N. El Karoui). Annales de l’Institut Henri Poincaré (B) Probability and Statistics 41(3), 269–283 (2004).
- Equilibria in Financial Markets with Heterogeneous Agents: A Probabilistic Perspective (with U. Horst and A. Kirman). Journal of Mathematical Economics 41(1–2), 123–155 (2005).
- American Options, Multi-armed Bandits, and Optimal Consumption Plans: A Unifying View (with P. Bank). In: Paris-Princeton Lecture Notes on Mathematical Finance, Lecture Notes in Mathematics, Vol. 1814, 1–42. Eds. Carmona, Cinlar, Ekeland, Jouini, Scheinkman, Touzi. Springer Verlag (2003).
- Stochastic Finance: An Introduction in Discrete Time (with A. Schied). de Gruyter Series in Mathematics 27, Berlin (2002, second revised edition 2004).
- Robust Preferences and Convex Measures of Risk (with A. Schied). In: Advances in Finance and Stochastics, Essays in Honor of Dieter Sondermann, 39–56. Eds. K. Sandmann, Ph. Schönbucher. Springer (2002).
- Convergence of Locally and Globally Interacting Markov Chains (with U. Horst). Stochastic Processes and their Applications 96(1), 99–121 (2001).
- Convex Measures of Risk and Trading Constraints (with A. Schied). Finance and Stochastics 6(4), 429–447 (2002).
- Probabilistic Aspects of Financial Risk. Plenary Lecture at the Third European Congress of Mathematics. Proceedings of the European Congress of Mathematics, Barcelona 2000, Birkhäuser (2001).
- Weak Brownian Motions of Arbitrary Order (with C. T. Wu, M. Yor). Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 36(4), 447–478 (2000).
- Efficient Hedging: Cost versus Shortfall Risk (with P. Leukert). Finance and Stochastics 4, 117–146 (2000).
- On Itô’s Formula for Multidimensional Brownian Motion (with Ph. Protter). Probab. Theory Relat. Fields 116, 1–20 (2000).
- Der Zufall in den Wirtschaftswissenschaften: Zur Rolle der Wahrscheinlichkeitstheorie in der Theorie der Finanzmärkte. Nova Acta Leopoldina NF 79, Nr. 308, 113–125 (1999).
- Canonical Decomposition of Linear Transformations of Two Independent Brownian Motions Motivated by Models of Insider Trading (with C. T. Wu, M. Yor). Stochastic Processes Appl. 84, 137–164 (1999).
- Quantile Hedging (with P. Leukert). Finance and Stochastics 3(3), 251–273 (1999).
- Richard von Mises (with U. Küchler). Mathematics in Berlin (Eds. H. G. W. Begehr, H. Koch, J. Kramer, N. Schappacher, E.-J. Thiele), 111–116. Birkhäuser (1998).
- Vom Leibniz-Kalkül zur stochastischen Analysis: Reines und Angewandtes aus der Mathematik zufälliger Schwankungen. Leopoldina (R.3) 43, 249–257 (1998).
- Ein Nobelpreis für Mathematik? DMV-Mitteilungen 1/98, 4–7 (1998).
- Optional Decomposition and Lagrange Multipliers (with Y. Kabanov). Finance & Stochastics 2(1), 69–81 (1998).
- Zur Versicherungsmathematik von Derivaten. Der Aktuar 3/4, 158–161 (1997).
- Optional Decompositions under Constraints (with D. Kramkov). Probab. Theory Relat. Fields 109, 1–25 (1997).
- Entropy Minimization and Schrödinger Processes in Infinite Dimensions (with N. Gantert). Annals of Probability 25, 901–926 (1997).
- Quadratic Covariation and an Extension of Itô’s Formula (with Ph. Protter and A. N. Shiryaev). Bernoulli 1, 149–169 (1995).
- Stock Price Fluctuation as a Diffusion in a Random Environment. Phil. Trans. R. Soc. Lond. A 347, 471–483 (1994).
- A Microeconomic Approach to Diffusion Models for Stock Prices (with M. Schweizer). Mathematical Finance 3(1), 1–23 (1993).
- Cancelling Anticipation by a Girsanov Transformation: A Paradox on Wiener Space (with P. Imkeller). Annales Inst. H. Poincaré 29(4), 569–586 (1993).
- Anticipating Girsanov Transformations: A Conditional Approach (with R. Buckdahn). Probab. Theory Relat. Fields 95, 311–330 (1993).
- Probabilistic Aspects of Options. Rolf Nevanlinna Institute Reports B6, Helsinki (1991).
- Orthogonal Martingale Representation (with R. J. Elliott). Stochastic Analysis, in honor of Moshe Zakai. Eds. E. Mayer-Wolf, E. Merzbach, A. Schwartz, Academic Press (1991).
- Martin Boundaries on Wiener Space. Diffusion Processes and Related Problems in Analysis, Vol. I. Ed. M. Pinsky, Progress in Probability 22, 3–16, Birkhäuser (1991).
- Hedging of Contingent Claims under Incomplete Information (with M. Schweizer). Applied Stochastic Analysis. Eds. M. H. A. Davis and R. J. Elliott, 389–414, Gordon and Breach, London (1990).
- Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading (with M. Schweizer). ASTIN Bulletin 18(2), 147–160 (1989).
- Large Deviations and Surface Entropy (with M. Ort). Colloque Paul Lévy sur les Processus Stochastiques. Astérisque 157/158, 173–190 (1988).
- Random Fields and Diffusion Processes. École d’Été de Probabilités de St. Flour XVI. Lecture Notes in Mathematics 1362, Springer, 101–203 (1988).
- Large Deviations for the Empirical Field of a Gibbs Measure (with S. Orey). Annals of Probability 16(3), 961–977 (1988).
- On Large Deviations and Relative Entropy of Markov Random Fields. Stochastic Differential Systems. Eds. H. J. Engelbert, W. Schmidt, Lecture Notes in Control and Information Sciences 96, Springer, 27–32 (1987).
- A Minimal Fluctuation Property for Coin Tossing and Locally Symmetric Martingales (with J. M. Clark). Stochastic Differential Systems. Lecture Notes in Control and Information Sciences 96, Springer, 333–337 (1987).
- Time Reversal and Smoothing of Infinite-dimensional Diffusion Processes (with J. D. Deuschel). Proc. 1st Int. Ascona-Como meeting, Stochastic Processes in Classical and Quantum Systems. Lecture Notes in Physics 262, Springer, 179–186 (1986).
- Hedging of Non-redundant Contingent Claims (with D. Sondermann). Contributions to Mathematical Economics. In Honor of G. Debreu. Eds. W. Hildenbrand and A. Mas-Colell, Elsevier Science Publ., North-Holland, 205–223 (1986).
- Time Reversal of Infinite-dimensional Diffusions (with A. Wakolbinger). Stochastic Processes and their Applications 22, 59–77 (1986).
- Time Reversal on Wiener Space. Stochastic Processes — Mathematics and Physics. Lecture Notes in Mathematics 1158, Springer, 119–129 (1986).
- An Entropy Approach to the Time Reversal of Diffusion Processes. Stochastic Differential Systems, Marseille-Luminy. Lecture Notes in Control and Information Sciences 69, Springer, 156–163 (1985).
- Von der Brownschen Bewegung zum Brownschen Blatt: Einige neuere Richtungen in der Theorie der stochastischen Prozesse. Perspectives in Mathematics, Anniversary of Oberwolfach 1984, Birkhäuser, 159–190 (1984).
- Almost Sure Convergence of Multiparameter Martingales for Markov Random Fields. Annals of Probability 12(1), 133–140 (1984).
- A Covariance Estimate for Gibbs Measures. J. of Functional Analysis 46(3), 387–395 (1982).
- Dirichlet Processes. Stochastic Integrals, Lecture Notes in Mathematics 851, Springer, 476–478 (1981).
- Calcul d’Itô sans Probabilités. Sém. Probabilités Strasbourg XV, Lecture Notes in Mathematics 850, Springer, 143–150 (1981).
- Macroscopic Convergence of Markov Chains on Infinite Product Spaces. In: Colloquia Mathematica Soc. Janos Bolyai 27, Random Fields, 363–371 (1979).
- Local Interactions with a Global Signal: A Voter Model. Biological Growth and Spread, Mathematical Theories and Applications. Lecture Notes in Biomathematics 38, Springer, 141–144 (1980).
- On the Global Markov Property. Quantum Fields — Algebras, Processes (Ed. L. Streit), Springer-Verlag Wien, 293–302 (1980).
- Tail Structure of Markov Chains on Infinite Product Spaces. Z. Wahrscheinlichkeitstheorie verw. Geb. 50, 273–285 (1979).
- Martingale Criteria for Stochastic Stability. Probability Theory, Banach Center Publications Vol. 5, Warsaw, 89–96 (1979).
- Quasimartingales à deux indices. C. R. Acad. Sc. Paris, t. 288, Sr. A, 61–64 (1979).
- On the Asymptotic Behavior of Stochastic Economic Processes (with M. Majumdar). J. of Mathematical Economics 5, 275–287 (1978).
- Zur Dynamik interdependenter Präferenzen. Quantitative Wirtschaftsforschung (Ed. H. Albach et al.), Mohr-Verlag Tübingen, 199–206 (1977).
- An “Inner” Variational Principle for Markov Fields on a Graph (with J. L. Snell). Z. Wahrscheinlichkeitstheorie verw. Geb. 39, 187–195 (1977).
- Martingales and Potential Theory. Proceedings of the Eight Brazilian Mathematical Colloquium, Pocos de Caldas 1971. Inst. Mat. Pura Apl., Rio de Janeiro, 131–140 (1977).
- The Bernoulli Principle and the Dirichlet Problem. Mathematical Economics and Game Theory, Essays in Honor of O. Morgenstern. Lecture Notes in Economics and Mathematical Systems 141, Springer, 208–217 (1977).
- A Liapunov Principle for Semimartingales. Proceedings of the AMS Symposia in Pure Mathematics, Vol. 31, 15–21 (1977).
- On the Potential Theory of Stochastic Fields. Bulletin of the International Statistical Institute Vol. 46, Invited Papers, 362–370 (1975).
- Stochastische Bewegungen und ihre ersten Integrale. Jahresber. Deutsch. Math. Verein. 76, 199–216 (1975).
- Phase Transition and Martin Boundary. Sém. Prob. Strasbourg IX, Lecture Notes in Mathematics 465, 305–317 (1975).
- Relative Densities of Semimartingales (with H. Airault). Inventiones Math. 27, 299–327 (1974).
- Random Economies with many Interacting Agents. J. of Mathematical Economics 1, 51–62 (1974).
- Stochastic Holomorphy. Mathematische Annalen 207, 245–255 (1974).
- On Entropy and Information Gain in Random Fields. Z. Wahrscheinlichkeitstheorie verw. Geb. 26, 207–217 (1973).
- On the Representation of Semimartingales. Annals of Probability 1(4), 580–589 (1973).
- Optimal Stopping of Constrained Brownian Motion. J. of Applied Probability 9, 557–571 (1972).
- The Exit Measure of a Supermartingale. Z. Wahrscheinlichkeitstheorie verw. Geb. 21, 154–166 (1972).
- Ein Littlewood-Kriterium für Martingale und insbesondere für Dirichlet-Lösungen. Elliptische Differentialgleichungen II (Ed. G. Anger), Akademie-Verlag Berlin, 113–118 (1971).
- Feine Topologie am Martinrand eines Standardprozesses. Z. Wahrscheinlichkeitstheorie verw. Geb. 12, 127–144 (1969).