Blar i NTNU Open på forfatter "Jakobsen, Espen Robstad"
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On distributional solutions of local and nonlocal problems of porous medium type
del Teso Mendez, Felix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2017)We present a theory of well-posedness and a priori estimates for bounded distributional (or very weak) solutions of ∂tu − L σ,µ[ϕ(u)] = g(x, t) in R N (0.1) × (0, T ), where ϕ is merely continuous and nondecreasing and L ... -
On fractional and nonlocal parabolic Mean Field Games in the whole space
Ersland, Olav; Jakobsen, Espen Robstad (Peer reviewed; Journal article, 2021)We study Mean Field Games (MFGs) driven by a large class of nonlocal, fractional and anomalous diffusions in the whole space. These non-Gaussian diffusions are pure jump Lévy processes with some σ-stable like behaviour. ... -
On nonlocal quasilinear equations and their local limits
Chasseigne, Emmanuel; Jakobsen, Espen Robstad (Journal article, 2017)We introduce a new class of quasilinear nonlocal operators and study equations involving these operators. The operators are degenerate elliptic and may have arbitrary growth in the gradient. Included are new nonlocal ... -
On Numerical Approximations of Fractional and Nonlocal Mean Field Games
Chowdhury, Indranil; Ersland, Olav; Jakobsen, Espen Robstad (Peer reviewed; Journal article, 2022)We construct numerical approximations for Mean Field Games with fractional or nonlocal diffusions. The schemes are based on semi-Lagrangian approximations of the underlying control problems/games along with dual approximations ... -
On numerical density approximations of solutions of SDEs with unbounded coefficients
Chen, Linghua; Jakobsen, Espen Robstad; Næss, Arvid (Journal article, 2017)We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and ... -
On the theory and numerical analysis of viscosity solutions
Jakobsen, Espen Robstad (Dr. ingeniøravhandling, 0809-103X; 2001:95, Doctoral thesis, 2001) -
On the well-posedness of solutions with finite energy for nonlocal equations of porous medium type
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Chapter, 2018)We study well-posedness and equivalence of different notions of solutions with finite energy for nonlocal porous medium type equations of the form ∂tu − Aϕ(u) = 0. These equations are possibly degenerate nonlinear diffusion ... -
Pricing European Options with Lévy Market Models and Deep Learning
Uv, Julie Johanne (Master thesis, 2019)I denne oppgaven har fem Lévy-modeller og et kunstig nevralt nettverk blitt implementert for å sammenligne prising av europeiske kjøpsopsjoner mot den geometrisk brownske bevegelsesdynamikken i Black-Scholes-formelen. ... -
Pricing Put Options using Heston's Stochastic Volatility Model
Våg, Andreas Brandsøy (Master thesis, 2013)The Heston model is a partial differential equation which is used to price options and is a further developed version of the more famous Black-Scholes equation. Heston considers stochastic volatility which results in an ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
Teso, Felix del; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2019)We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}^{\sigma,\mu}[\varphi(u)]=f \;\text{in}\; \mathbb{R}^ ... -
Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2018)We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $\partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t)$ in $\mathbb{R}^N\times(0,T),$ where ... -
Solution of the non-viscous Hamilton-Jacobi equation via vanishing viscosity
Cebatatauskas, Paulius (Bachelor thesis, 2022)Hovedmålet med denne oppgaven er å løse initialverdiproblemet for Hamilton-Jacobi(HJ) ligningen via forsvinnende viskositet, der Hamiltonen er H(Du) = |Du|^2. Vi antar at vår initialbetingelse er $g\in W^{2,\infty}(\R^n)$. ... -
Spectral Approximation of European and American Option Pricing Problems
Bruun, Frida Marie Eidsæther (Master thesis, 2018)In this thesis, properties of spectral methods applied to option pricing problems are inves-tigated. The Legendre Galerkin method with numerical integration is applied to Europeanand American option pricing problems under ... -
Spectral Discretizations of Option Pricing Models for European Put Options
Neset, Yngvild (Master thesis, 2014)The aim of this thesis is to solve option pricing models efficiently by using spectral methods. The option pricing models that will be solved are the Black-Scholes model and Heston's stochastic volatility model. We will ... -
Stochastic differential equations - A study on Levy processes
Ryalen, Pål Christie (Master thesis, 2015)The main goal of this thesis is to understand, describe, and implement some of the techniques and methods used in a research article by Kohatsu-Higa, Tankov, and Ortiz-Latorre on the subject of optimal simulation schemes ... -
The Dominative p-Laplacian and Sublinear Elliptic Operators
Brustad, Karl Kristian (Doctoral theses at NTNU;2018:128, Doctoral thesis, 2018)Utgangspunktet for avhandlingen er den såkaltep-Laplace-ligningen. Den er en andregrands partiell differensialligning (PDE), oger en ikke-lineær generalisering av den mer berømte Laplace-ligningen. I 2003 ble det oppdaget ... -
The Numerical Path Integration Method for Stochastic Differential Equations
Chen, Linghua (Doctoral thesis at NTNU;2016:219, Doctoral thesis, 2016) -
Towards a theory for fractional Mean Field Games in Hölder spaces
Bergset, Amund Skretting (Master thesis, 2023)I denne masteroppgaven studerer vi et Mean Field Game-system i hele rommet drevet av en fraksjonell Laplace-operator -(-∆)^(α/2) med orden α ∈ (1,2). Vi beviser eksistens og entydighet av klassiske løsninger til ... -
Uniform tail estimates and Lp(RN)-convergence for finite-difference approximations of nonlinear diffusion equations
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2022) -
Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type
del Teso, Félix; Endal, Jørgen; Jakobsen, Espen Robstad (Journal article; Peer reviewed, 2017)We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation ∂tu−Lμ[φ(u)]=0. Here Lμ can be any nonlocal symmetric degenerate ...