# 3 one period and multi period models replication and

• 104

This preview shows page 64 - 67 out of 104 pages.

3. One-period and multi-period models; replication and hedging. 4. Conditional expectations. 5. Martingales and Markov processes. 6. Change of measure. 7. Utility functions and the capital asset pricing model. 8. Stopping times and American derivatives. 9. Random walks and passage times.
Page 1 2015-2016 Math 3607 Mathematics 3607 Beginning Scientific Computing Autumn, Spring 3 credits Catalog Description: Introduction to uses of computers to solve problems arising in the physical and biological sciences, and in engineering and finance. Prerequisite: {C- or better in 2255, 2415, or 5520H; and C- or better in 2568 or 5520H}; or: {credit for 255, 415.xx, or 521H; and credit for 568, 571, or 520H}. Purpose: Math 3607 is a course which has three main goals: it introduces students to MATLAB (or improves their knowledge of MATLAB); it uses MATLAB to solve practical problems from various areas of mathematics, physics, engineering, business, and finance; and it presents the numerical analysis needed to use MATLAB effectively. The principle underlying this course is that the way to learn MATLAB and numerical analysis is by doing it, not by reading about it. This course is taught in a computer lab and MATLAB will be used to some extent every class. Textbook: Learning MATLAB, Problem Solving, and Numerical Analysis through Examples, by Ed Overman (downloadable e - book). Topics List: 1. MATLAB as a scalar calculator, round-off errors, debugging. 2. Arrays in MATLAB, probability theory, Markov processes. 3. Graphics in MATLAB, applications of probability theory, histograms. 4. Programming in MATLAB, more probability theory, mathematical biology. 5. Function m-files in MATLAB, more Markov processes, chaos. 6. More about functions, randomness. 7. Solving linear systems of equations. 8. Interpolation and approximation. 9. The solution of nonlinear equations and unconstrained optimization. 10. Numerical differentiation and integration 11. Time-evolution ordinary differential equations, boundary-value ordinary differential equations, stochastic differential equations, examples from many disciplines. 12. Eigenvalues, Fourier series.
Page 1 2015-2016 Math 3618 Mathematics 3618 Theory of Interest Autumn, Spring, Summer 3 credits Catalog Description: Financial transactions involving interest: measurement of interest, force of interest, annuities- certain, introduction to financial derivatives. Prerequisite: C- or better in 1152, 2162.xx, 1172, 2182H, 4181H; or credit for 153, 162, 162H, or 191H. Exclusions : Open only to actuarial science majors and pre-majors, and to math majors. Text : Mathematics of Investment & Credit , 5 th edition, by Broverman, published by Actex. ISBN: 9781566987677 Derivatives Markets , 2 nd edition, by McDonald, published by Pearson, ISBN: 9780321280305 Topics List: 1. Compound and simple rates of interest and discount, force of interest. 2. Annuity certain and annuity due. 3. Mortgage amortizations.
• • • 