MA680: Mathematical Modelling for Science and Finance

Mathematical Modelling and Computational Sciences at Laurier

Wilfrid Laurier University

Waterloo, Ontario,

Canada, N2L 3C5

• Basic Course Description
• Guidelines for Preparing Your Projects
• Additional References and Links

Projects in this course may include (pdf files describing the projects are given in the class):

• Modelling Volatility Smiles and Skews in Option Pricing with Jump-Diffusion Processes;
• Analysis of Nanostructure Properties with Continuum Mathematical Models of Elasticity;
• Linearization Techniques in Restoring the Information about Volatility Functions in the Asset Price Models;
• Mathematical Models of Calcium Waves in Biological Systems;
• Managing Risk in Option Portfolios: The Karhunen-Loeve Decomposition in Modelling Dynamics of Implied Volatility;
• Lie-Group Methods for Solving Differential Equations on Manifolds and Their Applications;
• Sparse Deconvolution, OPtimization Problems, and Nonlinear PDEs;
• Hamilton-Jacobi-Bellman-Isaacs Equation and Its Applications in Game Theory and Other Fields;
• Mathematical Models for Bacterial Organization and Their Applications to Modelling Cancer Development;
• Modeling Market Dynamics, Systemic Risk and Large Networks with Markov Chains: A PDE Approach;
• Other topics in applications of mathematical modelling tools in science, engineering, and finance.

Mathematical Modelling and Basic Software Links from Other Universities:

• Some MATLAB sofware for the solution of ODEs (Rice University);
• MATLAB programs for introductory PDE course (Oslo University);
• MATLAB codes for Numerical Mathematics (Politecnico Milano);
• Mathematical Modelling in Graduate Programs (Oxford University);
• Netlib software libraries;
• MATLAB Get Started Links (Iowa State);
• Your Report, Project or Thesis in LaTex (University of New Hampshire);
• LaTex tutorials (by Claudio Vellage).