Instructor: Fuh, Cheng-Der,
Graduate Institute of Statistics, National Central University and Institute of Statistical Science, Academia Sinica.
Office: 307 (Institute of Statistical Science). (o) 2783-5611 ext 307.
Email: stcheng@stat.sinica.edu.tw


Course outline.

1. Fundamental Concepts:
Definition and Basic Properties of Markov chains, Martingale and Brownian Motion, Sample Path Properties of Brownian Motion.

2. Ito Integration:
Definition of Ito Integration, Ito Formula, Stochastic Differential Equations, Continuous Time Finance Models.

3. Arbitrage Theory, Option Pricing and Financial Products:
Arbitrage Theory and Stochastic Differential Equations, Martingale Representation Theorems, Girsanov Theory (Change of Measure), Arbitrage Theory and Martingale, European Options and Black-Scholes Formula, Feynman-Kac Formula, American Options, Change of Numeraire.