http://publications.mfo.de/handle/mfo/4132 Tue, 07 Apr 2026 06:23:19 GMT 2026-04-07T06:23:19Z http://publications.mfo.de/handle/mfo/4189 Uncertainty as an Ingredient in Financial Modeling Korn, Ralf 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. Tue, 17 Dec 2024 00:00:00 GMT http://publications.mfo.de/handle/mfo/4189 2024-12-17T00:00:00Z Korn, Ralf 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. http://publications.mfo.de/handle/mfo/4163 Voronoi Cells: Or How to Find the Nearest Bakery Hess, Sarah; Torres, Angélica; van der Eyden, Mirte Deciding which mall, hospital or school is closest to us is a problem we face everyday. It even comes on holidays with us, when we optimize our plans to make sure that we have enough time to visit all the attractions we want to see. In this article, we show how concepts from metric algebraic geometry help us to rise to this task while planning a weekend trip to the Black Forest. Thu, 05 Sep 2024 00:00:00 GMT http://publications.mfo.de/handle/mfo/4163 2024-09-05T00:00:00Z Hess, Sarah Torres, Angélica van der Eyden, Mirte Deciding which mall, hospital or school is closest to us is a problem we face everyday. It even comes on holidays with us, when we optimize our plans to make sure that we have enough time to visit all the attractions we want to see. In this article, we show how concepts from metric algebraic geometry help us to rise to this task while planning a weekend trip to the Black Forest. http://publications.mfo.de/handle/mfo/4146 Randomness is Natural - an Introduction to Regularisation by Noise Djurdjevac, Ana; Elad Altman, Henri; Rosati, Tommaso Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this "regularisation by noise" phenomenon. Wed, 22 May 2024 00:00:00 GMT http://publications.mfo.de/handle/mfo/4146 2024-05-22T00:00:00Z Djurdjevac, Ana Elad Altman, Henri Rosati, Tommaso Differential equations make predictions on the future state of a system given the present. In order to get a sensible prediction, sometimes it is necessary to include randomness in differential equations, taking microscopic effects into account. Surprisingly, despite the presence of randomness, our probabilistic prediction of future states is stable with respect to changes in the surrounding environment, even if the original prediction was unstable. This snapshot will unveil the core mathematical mechanism underlying this "regularisation by noise" phenomenon. http://publications.mfo.de/handle/mfo/4133 Waves and Incidences Yung, Po-Lam The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem. Tue, 09 Apr 2024 00:00:00 GMT http://publications.mfo.de/handle/mfo/4133 2024-04-09T00:00:00Z Yung, Po-Lam The wave equation in Euclidean spaces describes many natural phenomena such as sound, light, or water waves. We explore how its solutions are related to the geometric problem of how long thin cylinders can intersect each other and discuss a related open problem.