mathematics

Hans Föllmer

Hans Föllmer is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hans Föllmer rather than just read about it. In short: Hans Föllmer (20 May 1941 in Heiligenstadt, Thuringia, Germany) is a German mathematician, currently professor emeritus at the Humboldt University of Berlin, visiting professor at the National University of Singapore, and Andrew D. White Professor-at-Large at Cornell University.

Key takeaways

Hans Föllmer belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hans Föllmer to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hans Föllmer from memory before moving on to harder problems.

Reference excerpt

Hans Föllmer (20 May 1941 in Heiligenstadt, Thuringia, Germany) is a German mathematician, currently professor emeritus at the Humboldt University of Berlin, visiting professor at the National University of Singapore, and Andrew D. White Professor-at-Large at Cornell University. He was awarded the Cantor medal in 2006. In 2007 he became doctor honoris causa at the Paris Dauphine University. Föllmer is widely known for his contributions to probability theory, stochastic analysis and mathematical finance. In mathematical economics, he made early contributions to the mathematical modeling of social interactions. In mathematical finance, he made fundamental contributions to the theory of risk measures and the hedging of contingent claims. The Föllmer process, a stochastic process first considered by Erwin Schrödinger but formulated in the language of stochastic differential equations by Föllmer, is named after him. In mathematical finance, the Föllmer-Schweizer decomposition is named after him and Martin Schweizer.

Main scientific works Föllmer, Hans (March 1974). "Random economies with many interacting agents". Journal of Mathematical Economics. 1 (1): 51–62. doi:10.1016/0304-4068(74)90035-4. ISSN 0304-4068. Föllmer, H. (1981). "Calcul d'Ito sans probabilites". Séminaire de Probabilités XV 1979/80. Lecture Notes in Mathematics. Vol. 850. Springer Berlin Heidelberg. pp. 143–150. doi:10.1007/BFb0088364. eISSN 1617-9692. ISBN 978-3-540-10689-0. ISSN 0075-8434. Föllmer, Hans (1988). "Random fields and diffusion processes". Lecture Notes in Mathematics. Vol. 1362. Springer Berlin Heidelberg. pp. 101–203. doi:10.1007/BFb0086180. eISSN 1617-9692. ISBN 978-3-540-50549-5. ISSN 0075-8434. Föllmer, Hans; Schied, Alexander (25 July 2016), Stochastic Finance, De Gruyter, doi:10.1515/9783110463453, ISBN 9783110463453 Föllmer, Hans; Schied, Alexander (1 October 2002). "Convex measures of risk and trading constraints". Finance and Stochastics. 6 (4): 429–447. doi:10.1007/s007800200072. hdl:10419/62741. ISSN 0949-2984. S2CID 1729029. Föllmer, H.; Kabanov, Y.M. (1 November 1997). "Optional decomposition and Lagrange multipliers". Finance and Stochastics. 2 (1): 69–81. doi:10.1007/s007800050033. eISSN 1432-1122. hdl:10419/66314. ISSN 0949-2984. S2CID 13051630.

References

Illustrations

Worked examples

Example 1 — a first encounter with Hans Föllmer

Start with the simplest possible case. Write down what Hans Föllmer claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hans Föllmer before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hans Föllmer ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hans Föllmer

In research: Hans Föllmer appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hans Föllmer in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hans Föllmer is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1941 births, 20th-century German mathematicians, 21st-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hans Föllmer outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hans Föllmer in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hans Föllmer means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hans Föllmer out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hans Föllmer in simple terms?

Why does Hans Föllmer matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hans Föllmer?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hans Föllmer.