金融市場的隨機分析   (89年度 下學期)

The goal of this course is introduce some basic method and results of financial computations with derivative securities. Two approaches will be studied. A. Black-Scholes model. The market is treated as a continuous time stochastic process. By employing （geometric）Brownian motion and Ito's formula, the diffusion equation governing the prices of the derivatives is derived and solved. B. Cox-Ross-Rubinstein model. The market is viewed as a discrete time process. The basic tools here are （semi）martingales, stochastic exponents, and Girsanov's theorem.

A. The mathematics of financial derivatives. By P. Wilmott, S. Howison and J. Dewynne. Cambridge University Press, 1977 B. Options, Futures and other derivatives. By J. C. Hull. Prentice Hall, 3rd edition. 1998 C. Financial markets. By A. V. Melnikov. Translations of Math1. Monographs, volume 184. AMS. 1999 D. Principles of infinitesimal stochastic and financial analysis. By Imme van den Berg. World Scientific, 2000

習題

必先修Calculus, basic probability