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.
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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.
Vis fullstendig beskrivelse