THIRD SEMESTERcoretheorySem 3
MATHEMATICS FOR FINANCE
MAT 2132
Syllabus
- 01The geometry of linear equations, elimination with matrices, multiplication and inverse matrices, factorisation into A=LU, Transpose, permutation of matrices, vector space, Column Space and Null Space, Solving Ax=0: Pivot variables, special solutions; Solving Ax=b: Row reduced form, independence, basis and dimension, independence, basis and dimension, Projection matrices and least squares, orthogonal matrices and Gram- Schmidt orthogonalization, Eigen Values and Eigen vectors, Diagonalisation and powers of matrix A, Markov matrices, Symmetric matrices and positive definite matrices, similar matrices and Jordan form, Singular value decomposition, Linear transformation, and their matrices
- 02Introduction to systems of first-order linear differential equations, Solution techniques: Matrix methods, eigenvalues, eigenvectors, Applications in finance and technology: modeling interconnected systems, Markov chains, etc. Modeling financial derivatives using differential equations (Black-Scholes equation, etc.). Differential equations in risk management and portfolio optimization
- 03Introduction to PDEs: Classification (elliptic, parabolic, hyperbolic). Boundary value problems and initial value problems. Applications in option pricing, stochastic calculus, and quantitative finance. Solution Methods: Laplace transform/ Fourier transform
- 04Numerical Methods for Differential Equations: Finite difference methods for solving partial differential equations. Monte Carlo simulations in financial modeling
- 05Stochastic differential equations in financial mathematics. Control theory applications in financial technology
References
- D. C Lay, Linear algebra and its applications, Pearson, 2014
- Gilbert Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, 2000
- William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems, John Wiley & Sons, Inc., 2009
- Stanley J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications Inc., 2003
- Bernt Oksendal, Stochastic Differential Equations- An Introduction with Applications, Springer Berlin Heidelberg, 2013
Credits Structure
4Lecture
0Tutorial
0Practical
4Total