Cristin-prosjekt-ID: 395
Sist endret: 11. desember 2014, 14:15

Cristin-prosjekt-ID: 395
Sist endret: 11. desember 2014, 14:15
Prosjekt

Integro-PDEs: Numerical methods, Analysis, and Applications to Finance

prosjektleder

Espen Robstad Jakobsen
ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

prosjekteier / koordinerende forskningsansvarlig enhet

  • Senter for matematikk for anvendelser ved Universitetet i Oslo
  • Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

Finansiering

  • Norges forskningsråd
    Prosjektkode: 176877

Klassifisering

Vitenskapsdisipliner

Analyse • Anvendt matematikk • Matematisk modellering og numeriske metoder

Kategorier

Prosjektkategori

  • Grunnforskning

Kontaktinformasjon

Tidsramme

Avsluttet
Start: 1. august 2006 Slutt: 31. desember 2010

Beskrivelse Beskrivelse

Tittel

Integro-PDEs: Numerical methods, Analysis, and Applications to Finance

Sammendrag

Integro-PDEs: Numerical methods, Analysis, and Applications to Finance is a research project sponsored by the eVita programme of the Research Council of Norway. Participants are Associate Professor E. R. Jakobsen (Department of Mathematical Sciences, NTNU) and Professor K. H. Karlsen (Centre of Mathematics for Applications, University of Oslo). The 3 year Researcher project consists of one doctoral position (3 years, at NTNU), one post-doctoral position (2 years), and funding for equipment, travels, and guests. The goal is to study integro partial differential equations (integro-PDEs) appearing in optimal stochastic control theory. Today the most important application of optimal stochastic control theory is to finance. Mathematical finance is internationally one of the fastest growing areas of research and its practical applications to the problem of pricing derivatives and determining optimal portfolios are numerous. Since the discovery of the famous Black-Scholes equation in the 1970's there has been a rush in the development of sophisticated models for options and optimal portfolio selections. Due to their complexity these models cannot be solved analytically, and therefore we must resort to numerical methods. Solving such integro-PDEs numerically is computationally demanding due to the fact that they can be non-local, non-linear, degenerate, and multi-dimensional at the same time. Numerical methods are the main focus of this project. We plan to develop, implement, and analyze efficient and robust general purpose numerical methods for such equations; we plan to develop a framework for error estimates for such methods; and we plan to solve numerically specific problems from finance. We also want to pursue theoretical studies that are related to, and important for numerical analysis, namely studies into regularity of solutions and boundary value problems.

Vitenskapelig sammendrag

Integro-PDEs: Numerical methods, Analysis, and Applications to Finance is a research project sponsored by the eVita programme of the Research Council of Norway. Participants are Associate Professor E. R. Jakobsen (Department of Mathematical Sciences, NTNU) and Professor K. H. Karlsen (Centre of Mathematics for Applications, University of Oslo). The 3 year Researcher project consists of one doctoral position (3 years, at NTNU), one post-doctoral position (2 years), and funding for equipment, travels, and guests. The goal is to study integro partial differential equations (integro-PDEs) appearing in optimal stochastic control theory. Today the most important application of optimal stochastic control theory is to finance. Mathematical finance is internationally one of the fastest growing areas of research and its practical applications to the problem of pricing derivatives and determining optimal portfolios are numerous. Since the discovery of the famous Black-Scholes equation in the 1970's there has been a rush in the development of sophisticated models for options and optimal portfolio selections. Due to their complexity these models cannot be solved analytically, and therefore we must resort to numerical methods. Solving such integro-PDEs numerically is computationally demanding due to the fact that they can be non-local, non-linear, degenerate, and multi-dimensional at the same time. Numerical methods are the main focus of this project. We plan to develop, implement, and analyze efficient and robust general purpose numerical methods for such equations; we plan to develop a framework for error estimates for such methods; and we plan to solve numerically specific problems from finance. We also want to pursue theoretical studies that are related to, and important for numerical analysis, namely studies into regularity of solutions and boundary value problems.

prosjektdeltakere

prosjektleder
Aktiv cristin-person

Espen Robstad Jakobsen

  • Tilknyttet:
    Prosjektleder
    ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

Hilde Sande Borck

  • Tilknyttet:
    Prosjektdeltaker
    ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

Simone Cifani

  • Tilknyttet:
    Prosjektdeltaker
    ved Institutt for matematiske fag ved Norges teknisk-naturvitenskapelige universitet

Kenneth Aksel Hvistendahl Karlsen

  • Tilknyttet:
    Prosjektdeltaker
    ved Matematisk institutt ved Universitetet i Oslo
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Resultater Resultater

Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations.

Debrabant, Kristian; Jakobsen, Espen Robstad. 2014, American Institute of Mathematical Sciences (AIMS) Press. SDU, NTNUVitenskapelig Kapittel/Artikkel/Konferanseartikkel

Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations.

Debrabant, Kristian; Jakobsen, Espen Robstad. 2012, Fourteenth International Conference devoted to Theory, Numerics and Applications of Hyperbolic Problems – HYP2012. SDU, NTNUVitenskapelig foredrag

Semi-Lagrangian schemes for linear and fully non-linear diffusion equations.

Debrabant, Kristian; Jakobsen, Espen Robstad. 2013, Mathematics of Computation. SDU, NTNUVitenskapelig artikkel

On the spectral vanishing viscosity method for periodic fractional conservation laws.

Jakobsen, Espen Robstad; Cifani, Simone. 2013, Mathematics of Computation. NTNUVitenskapelig artikkel

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations.

Cifani, Simone; Jakobsen, Espen Robstad; Karlsen, Kenneth Hvistendahl. 2011, BIT Numerical Mathematics. NTNU, UIOVitenskapelig artikkel
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