Mathematical Foundations for Finance：Wash U Finance Slides

1389

收藏 2010-01-29

Thiscourse covers mathematical foundations that are essential for advanced
quantitative finance courses. The maincontents include:

(1)
MatrixAlgebra: The operations of matrices, definite matrices, inverse of squaredmatrices, and applications in solving linear systems will be covered.
(2)
MatrixCalculus:
Students will learn how toderive the derivatives of vector functions.
(3)
NumericalMethods for Solving Nonlinear Equations: Bisection, Newton’s Method, SecantMethod will be covered and solving nonlinear equations in Matlab will also becovered.
(4)
Unconstrainedand Constrained Optimization: The first order and second order conditions forsingle and multiple variables unconstrained optimization and Kuhn-Tuckerconditions for constrained optimization will be covered.
(5)
NumericalOptimization:
Students will learn how touse Optimization Toolbox of Matlab to solve unconstrained optimization problem,quadratic programming and nonlinear optimization with constraints. Thealgorithm of Quasi-Newton method and Sequential Quadratic Programming will bebriefly mentioned.
(6)
OrdinaryDifferential Equations: Students will learn how to solve first and second orderlinear ordinary differential equations.
(7)
NumericalOrdinary Differential Equations: We will cover Taylor Series methods andRunge-kutta methods and learn how to solve ordinary differential equations inMatlab.
(8)
PartialDifferential Equations: Black-Scholes PDE can be reduced to an initial valueproblem of a heat equation. Students will learn how to solve the initial valueproblems of heat equations using Fourier Transform. Students will also learnhow to solve the initial and boundary value problems of heat equations usingseparation of variables.
(9)
Numerical PartialDifferential Equations: Students will learn how to solve partial differentialequations using explicit and implicit finite difference methods. Solving partialdifferential equations in Matlab will also be covered.

(10) Probability and Statistics: We willcover random variables, probability density

functions, expectations, variances and covariance, bivariatenormal distributions,

exponentialdistributions, etc.

附件列表

mathematical foundations for finance.rar