Uncertainty as an ingredient in financial modeling

Snapshots of modern mathematics from Oberwolfach

Uncertainty as an ingredient in financial modeling

Uncertainty – as opposed to risk – is used to describe events to which we are not able to assign a probability due to lack of information. Instead of assigning a probability to an uncertain event, we only assume that such an event is possible or that its probability is within some range. We illustrate the effects of the inclusion of uncertainty in modeling by looking at simple cases of an optimal investment problem.

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Mathematical subjects

Probability Theory and Statistics

Connections to other fields

Finance
Humanities and Social Sciences

Author(s)

Ralf Korn

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DOI (Digital Object Identifier)

10.14760/SNAP-2024-004-EN

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snapshot-2024-004.pdf

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snapshots: overview

Ralf Korn
Uncertainty as an ingredient in financial modeling
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4 = 2 × 2, or the power of even integers in Fourier analysis
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Algebras and quantum games
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Felder und Räume: Symmetrie und Lokalität in Mathematik und theoretischen Wissenschaften
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The periodic tables of algebraic geometry
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Patterns and waves in theory, experiment, and application
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Closed geodesics on surfaces
Kathrin Hellmuth, Christian Klingenberg
Route planning for bacteria
Fabian Mussnig
Characterizations of intrinsic volumes on convex bodies and convex functions
Jennifer S. Balakrishnan
A tale of three curves
Michael Baake, Uwe Grimm, Robert V. Moody
What is Pattern?
Saiteja Utpala, Nina Miolane
Biological Shape Analysis with Geometric Statistics and Learning
Ilya Dumanski, Valentina Kiritchenko
Representations and degenerations
Jonas Latz, Björn Sprungk
Solving inverse problems with Bayes’ theorem
Herbert Gangl
Jewellery from tessellations of hyperbolic space
Chr istina Frederick, Yunan Yang
Seeing through rock with help from optimal transport
David A. Craven
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Hugh Thomas
The Robinson–Schensted algorithm
Franca Hoffmann, Sara Merino-Aceituno
Emergence in biology and social sciences
Jason D. Lotay
Lagrangian mean curvature flow
Leo Storme
Finite geometries: pure mathematics close to applications
Francesca Arici, Bram Mesland
Describing distance: from the plane to spectral triples
Martijn Caspers
Quantum symmetry
Fadoua Balabdaoui, Yulia Kulagina
The Enigma behind the Good–Turing formula
Anna Haensch
Reflections on hyperbolic space
Isaac Goldbring
Ultrafilter methods in combinatorics
Gandalf Lechner
Zopfgruppen, die Yang–Baxter-Gleichung und Unterfaktoren
Baptiste Rognerud
Invitation to quiver representation and Catalan combinatorics
Po-Ling Loh
Searching for structure in complex data: A modern statistical quest
David Kerr
C∗-algebras: structure and classification
Sara Lamboglia, Martin Ulirsch
From the dollar game to the Riemann-Roch Theorem
Steven Rayan, Laura P. Schaposnik
Higgs bundles without geometry
Behrend Heeren, Martin Rumpf
Shape space - a paradigm for character animation in computer graphics
Joshua Zahl
Rotating needles, vibrating strings, and Fourier summation
Moritz Weber
Quantum symmetry
Christian Berg
Determinacy versus indeterminacy
Jayadev S. Athreya, David Aulicino
Vertex-to-Self Trajectories on the Platonic Solids
Gianluca Finocchio
Random matrix theory: Dyson Brownian motion
Holger Kammeyer, Roman Sauer
From Betti numbers to l2-Betti numbers
Martin J. Gander
Is it possible to predict the far future before the near future is known accurately?
Jan-Bernhard Kordaß
The Interaction of Curvature and Topology
barbara Kaltenbacher, Igor Kukavica, Irena Lasiecka, Roberto Triggianti, Amjad Fuffaha, Justin Weber
The Mathematics of Fluids and Solids
Jake Fillman, Tom van den Boom
A surprising connection between quantum mechanics and shallow water waves
Daniel Zelazo, Shiyu Zhao
Formation Control and Rigidity Theory
Ana Khukhro
Expander graphs and where to find them
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Deep Learning and Inverse Problems
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Mixed-dimensional models for real-world applications
Pietro Milici
Touching the transcendentals: tractional motion from the birth of calculus to future perspectives
Loïc Petitgirard
Analogue mathematical instruments: Examples from the “theoretical dynamics” group (France, 1948–1964)
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Configuration spaces and braid groups
Tereza Klimošová
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On Logic, Choices and Games
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Nonlinear Acoustics
Volker Betz
Random permutations
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Counting self-avoiding walks on the hexagonal lattice
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Algebra, matrices, and computers
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Positive Scalar Curvature and Applications
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Diophantine equations and why they are hard
Martin Buhmann, Janin Jäger
On radial basis functions
Ralf Schiffler
Snake graphs, perfect matchings and continued fractions
Nicolai Baldin
Estimating the volume of a convex body
Liran Rotem
Mixed volumes and mixed integrals
Filippo Santambrogio
A short story on optimal transport and its many applications
Sebastian Schönnenbeck
Number theory in quantum computing
Matthias Morzfeld, Sebastian Reich
Data assimilation: mathematics for merging models and data
Claus Hertling
Geometry behind one of the Painlevé III differential equations
Antonio Lerario
The codimension
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The mathematics of aquatic locomotion
Erwan Brugallé, Ilia Itenberg, Kristin Shaw, Oleg Viro
Tropical geometry
Alex Barnett
Fast Solvers for Highly Oscillatory Problems
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Thomas Sauer
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Piotr Sułkowski
Topological recursion
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The Algebraic Statistics of an Oberwolfach Workshop
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Solving quadratic equations in many variables
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Mathematics plays a key role in scientific computing
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Spaces of Riemannian metrics
Shaula Fiorelli Vilmart, Gilles Vilmart
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Justin Solomon
Computational Optimal Transport
Justyna Szpond
A few shades of interpolation
George Hagedorn, Caroline Lasser
Molecular quantum dynamics
Marco Radeschi
Closed geodesics on surfaces and Riemannian manifolds
Christian Engwer, Markus Knappitsch
Mathematische Modellierung von Krebswachstum
Michael Baake, David Damanik, Uwe Grimm
Aperiodic Order and Spectral Properties
Lukas Pottmeyer
News on quadratic polynomials
Felix Günther
Winkeltreue zahlt sich aus
Jacob Bedrossian
Towards a Mathematical Theory of Turbulence in Fluids
Laurent Bartholdi
Profinite groups
Dietmar Gallistl
The adaptive finite element method
Steven Klee
Footballs and donuts in four dimensions
Nikolai Nowaczyk
The Willmore Conjecture
Lior Bary-Soroker
Prime Tuples in Function Fields
Rafael Guglielmetti, Matthieu Jacquemet
Polyhedra and commensurability
Manfred Deistler, Andreas Graef
Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse
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Symmetry and characters of finite groups
Maria Dostert, Stefan Krupp, Jan Hendrick Rolfes
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Tomasz Szemberg
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Éric Fusy
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Magnus Egerstedt
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Ulrich Krähmer
From computer algorithms to quantum field theory: an introduction to operads
Juanjo Rué
Domino tilings of the Aztec Diamond
Sebastian Funk
The mystery of sleeping sickness – why does it keep waking up?
Antti Knowles
Quantum diffusion
Amanda Swan, Albert Murtha
Modelling the spread of brain tumours
J. Marron
Visual Analysis of Spanish Male Mortality
Christopher Sangwin
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Jürg Kramer, Anna-Maria Pippich
Special values of zeta functions and areas of triangles
Victoria Powers
How to choose a winner : the mathematics of social choice
Valentina Kiritchenko, Evgeny Smirnov, Vladlen Timorin
Ideas of Newton-Okounkov bodies
Ben Schweizer
Darcy’s law and groundwater flow modelling
Raluca Eftimie
Modelling communication and movement: from cells to animals and humans
Tom Solomon
Chaos and chaotic fluid mixing
Thorsten Holm
Friezes and tilings
George Willis
Zero-dimensional symmetry
Christine Breiner
Minimizing energy
Diana Davis
Billiards and flat surfaces
Peter Benner, Hermann Mena, René Schneider
Drugs, herbicides, and numerical simulation
Gregory Knese
Operator theory and the singular value decomposition
Alain Valette
The Kadison-Singer problem
Ragnar-Olaf Buchweitz, Eleonore Faber
Swallowtail on the shore
Howell Tong
Statistics and dynamical phenomena
Brian Harbourne, Thomas Szemberg
Arrangements of lines
Bruce Reznick
What does ">" really mean?
Harald Helfgott
The ternary Goldbach Problem
Wolfgang Lerche
Matrixfaktorisierungen
John E. McCarthy
Dirichlet Series

Mathematical subjects

Algebra and Number Theory
Analysis
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Finance
Humanities and Social Sciences
Life Science
Physics
Reflections on Mathematics

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