Essays about: "Stochastic differential equation"

Showing result 1 - 5 of 30 essays containing the words Stochastic differential equation.

1. 1. Improved Statistical Methods for Elliptic Stochastic Homogenization Problems : Application of Multi Level- and Multi Index Monte Carlo on Elliptic Stochastic Homogenization Problems

   University essay from Uppsala universitet/Tillämpad beräkningsvetenskap

   Author : Khalil Daloul; [2023]
   Keywords : Homogenization; Multilevel Monte Carlo; Multi-Index Monte Carlo; Monte Carlo; Multiscale methods;

   Abstract : In numerical multiscale methods, one relies on a coupling between macroscopic model and a microscopic model. The macroscopic model does not include the microscopic properties that the microscopic model offers and that are vital for the desired solution. 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. Stochastic Runge–Kutta Lawson Schemes for European and Asian Call Options Under the Heston Model

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

   Author : Nicolas Kuiper; Martin Westberg; [2023]
   Keywords : Runge–Kutta Lawson scheme; Heston model; Black–Scholes model; Stochastic Differential Equation; Euler–Maruyama scheme; Midpoint scheme; Monte Carlo; European Options; Asian Options; Option pricing.;

   Abstract : This thesis investigated Stochastic Runge–Kutta Lawson (SRKL) schemes and their application to the Heston model. Two distinct SRKL discretization methods were used to simulate a single asset’s dynamics under the Heston model, notably the Euler–Maruyama and Midpoint schemes. 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