Seminari - Dipartimento Computer Science Seminari - Dipartimento Computer Science validi dal 29.02.2024 al 01.03.2025. Numerical method for Mathematical finance Relatore: Silvia Lavagnini; Provenienza: Oslo University - Department of Data Science and Analytics Nydalsveien; Data inizio: 2024-05-13; Referente interno: Luca Di Persio; Riassunto: In this mini-course we will discuss various numerical methods for the pricing of financial instruments, with a particular focus on applications to the energy markets. We will start from the simulations of some of the most common continuous-time models, such as the geometric Brownian motion and the Ornstein-Uhlenbeck process. Stochastic volatility models, such as the Heston model, may also be discussed. We will then consider different approaches for options pricing, such as the PDE and the Monte Carlo approach. State-dependent options may also be discussed. Finally, forward contracts with delivery period typical of the energy markets will be treated from the Heath-Jarrow-Morton modelling point of view. If time allows, we will also discuss (simulations of) SPDEs for Hilbert space-valued forward curves. The course will be given in Python. Mon, 13 May 2024 00:00:00 +0200 Numerical methods for uncertainty quantification [MAT08, 2 ECTS] Relatore: Chiara Piazzola; Provenienza: Technical University of Munich; Data inizio: 2024-04-03; Note orario: (starting from, 2 weeks); Referente interno: Marco Caliari; Riassunto: The aim of this course is to provide an introduction to uncertainty quantification for differential equations with random coefficients. We will focus on the forward problem of assessing the propagation of the uncertainty in the input coefficients to the solution of the equation and discuss some standard and state-of-the-art computational methods, such as the Monte Carlo method, sparse grids, and the polynomial chaos expansion. Moreover, we will address multi-fidelity techniques, such as the multi-level Monte Carlo method and multi-index stochastic collocation, that leverage low and high-fidelity model solutions to achieve the best trade-off between accuracy and computational cost. To complement the discussion, we will present some real-world applications. . Wed, 3 Apr 2024 00:00:00 +0200 Modeling the "biotic pump": quantifying the role of ecosystem transpiration in water cycle and temperature mitigation Relatore: Ugo Bardi; Provenienza: Università di Firenze; Data inizio: 2024-03-19; Ora inizio: 15.00; Note orario: Sala Verde (presenza e remoto); Referente interno: Davide Quaglia; Riassunto: The terrestrial water cycle links the soil and atmosphere moisture reservoirs through four fluxes: precipitation, evaporation, runoff, and atmospheric moisture convergence (net import of water vapor to balance runoff). Each of these processes is essential for sustaining human and ecosystem well-being. Predicting how the water cycle responds to changes in vegetation cover remains a challenge. Recently, changes in plant transpiration across the Amazon basin were shown to be associated disproportionately with changes in rainfall, suggesting that even small declines in transpiration (e.g., from deforestation) would lead to much larger declines in rainfall. Here, constraining these findings by the law of mass conservation, we show that in a sufficiently wet atmosphere, forest transpiration can control atmospheric moisture convergence such that increased transpiration enhances atmospheric moisture import and results in water yield. Conversely, in a sufficiently dry atmosphere increased transpiration reduces atmospheric moisture convergence and water yield. Modeling the potential of vegetation for enhancing moisture convergence is crucial for characterizing the consequences of deforestation as well as for motivating and guiding ecological restoration. Join Zoom Meeting Meeting ID: 953 8364 9556 Passcode: 213844 Referente: Davide Quaglia . Tue, 19 Mar 2024 15:00:00 +0100 Microscopic and macroscopic traffic models for low- and high-density crowds Relatore: Emiliano Cristiani; Provenienza: CNR- IAC, Roma; Data inizio: 2024-03-06; Ora inizio: 16.30; Note orario: Aula G; Referente interno: Giacomo Albi; Riassunto: Microscopic and macroscopic traffic models for low- and high-density crowds In this talk we deal with pedestrian modeling, aiming at simulating crowd behavior in normal and emergency scenarios, including highly congested mass events. We present two models: the first one isan microscopic(agent-based), continuous-in-space, discrete-in-time, nondifferential model, where pedestrians have finite size and are compressible to a certain extent. The model also takes into account the pushing behavior appearing at extremely high densities.The model is able to reproduce the concave/concave fundamental diagram with a quot;double humpquot; (i.e. with a second peak) which shows up when body forces come into play. The second model is a possible macroscopic and PDE-based counterpart of the first model, devised to save computationaltime while preserving all the good features. Joint work with Laura Bartoli and Simone Cacace. Wed, 6 Mar 2024 16:30:00 +0100