Xinfu Chen Mathematical Finance II
Xinfu Chen Mathematical Finance II Department of mathematics, University of Pittsburgh Pittsburgh, PA 15260, USA ii MATHEMATICAL FINANCE II Course Outline This course is an introduction to modern mathematical ¯nance. Topics include 1. single period portfolio optimization based on the mean-variance analysis, capital asset pricing model, factor models and arbitrage pricing theory. 2. pricing and hedging derivative securities based on a fundamental state model, the well-received Cox-Ross-Rubinstein's binary lattice model, and the celebrated Black-Scholes continuum model; 3. discrete-time and continuous-time optimal portfolio growth theory, in particular the universal log- optimal pricing formula; 4. necessary mathematical tools for ¯nance, such as theories of measure, probability, statistics, and stochastic process. Prerequisites Calculus, Knowledge on Excel Spreadsheet, or Matlab, or Mathematica, or Maple. Textbooks David G. Luenberger, Investment Science, Oxford University Press, 1998. Xinfu Chen, Lecture Notes, available online www.math.pitt.edu/~xfc. Recommended References Steven Roman, Introduction to the Mathematics of Finance, Springer, 2004. John C. Hull, Options, Futures and Other Derivatives, Fourth Edition, Prentice-Hall, 2000. Martin Baxter and Andrew Rennie, Financial Calculus, Cambridge University Press, 1996. P. Wilmott, S. Howison & J. Dewynne, The Mathematics of Financial Derviatives, CUP, 1999. Stanley R. Pliska, Inroduction to Mathematical Finance, Blackwell, 1999. Grading Scheme Homework 40 % Take Home Midterms 40% Final 40% iii iv MATHEMATICAL FINANCE II Contents MATHEMATICAL FINANCE II iii 1 Mean-Variance Portfolio Theory 1 1.1 Assets and Portfolios . 1 1.2 The Markowitz Portfolio Theory . 9 1.3 Capital Asset Pricing Model . 14 1.3.1 Derivation of the Market Portfolio .
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