Essays about: "stochastic differential equations"

Showing result 1 - 5 of 39 essays containing the words stochastic differential equations.

1. 1. Itô Diffusions on Level Sets

   University essay from Uppsala universitet/Analys och partiella differentialekvationer; Uppsala universitet/Statistik, AI och data science

   Author : Coën Olofsson; [2023]
   Keywords : Itô diffusions; level sets; stochastic differential geometry; numerical schemes;

   Abstract : Itô diffusions that move on level sets of functions in Rn, which we have called level processes, are an overlooked variant of the classical Itô processes. These processes find themselves nestled between the study of regular Itô diffusions in Rn and diffusions which are bound to smooth manifolds. READ MORE

3. 2. Merton's Portfolio Problem under Jourdain--Sbai Model

   University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

   Author : Sajedeh Saadat; [2023]
   Keywords : Merton’s Optimal Investment-Consumption Problem; Dynamic Programming; Hamilton-Jacobi-Bellman equation; Stochastic Volatility Model; Finite-difference method; Crank-Nicolson.;

   Abstract : Portfolio selection has always been a fundamental challenge in the field of finance and captured the attention of researchers in the financial area. Merton's portfolio problem is an optimization problem in finance and aims to maximize an investor's portfolio. READ MORE

4. 3. Exploring backward stochastic differential equations and deep learning for high-dimensional partial differential equations and European option pricing

   University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

   Author : Jonathan Leung; [2023]
   Keywords : Backward Stochastic Differential Equations; Semilinear Parabolic Partial Differential Equations; Artificial Neural Networks; Nonlinear Option Pricing; Black-Scholes; Nonlinear Feynman-Kac; Euler-Maruyama;

   Abstract : Many phenomena in our world can be described as differential equations in high dimensions. However, they are notoriously challenging to solve numerically due to the exponential growth in computational cost with increasing dimensions. READ MORE

5. 4. On the Modelling of Stochastic Gradient Descent with Stochastic Differential Equations

   University essay from Uppsala universitet/Analys och partiella differentialekvationer

   Author : Martin Leino; [2023]
   Keywords : stochastic gradient descent; stochastic differential equations; statistical machine learning;

   Abstract : Stochastic gradient descent (SGD) is arguably the most important algorithm used in optimization problems for large-scale machine learning. Its behaviour has been studied extensively from the viewpoint of mathematical analysis and probability theory; it is widely held that in the limit where the learning rate in the algorithm tends to zero, a specific stochastic differential equation becomes an adequate model of the dynamics of the algorithm. READ MORE

6. 5. Moving in the dark : Mathematics of complex pedestrian flows

   University essay from Karlstads universitet/Fakulteten för hälsa, natur- och teknikvetenskap (from 2013)

   Author : Meghashyam Veluvali; [2023]
   Keywords : Mathematical modelling of pedestrian dynamics; stochastic systems; evacuation time; random walk method; parabolic equation; finite difference method;

   Abstract : The field of mathematical modelling for pedestrian dynamics has attracted significant scientific attention, with various models proposed from perspectives such as kinetic theory, statistical mechanics, game theory and partial differential equations. Often such investigations are seen as being a part of a new branch of study in the domain of applied physics, called sociophysics. READ MORE