Pre-requisite
MAT 135AB

Texts

• Bernt Oksendal: Stochastic Differential Equations Springer-Verlag; 6th edition (2003)
  
• Steven E. Shreve: Stochastic Calculus for Finance II: Continuous-Time Models (Springer Finance) 2008

• Brownian motion: random walks, quadratic variation, first passage time.
• Ito integral and Stratonovitch integral
• Ito formula
• Martingale
• Stochastic differential equations
• Applications: Black-Schole equation and formula, Kalman filter, Kolmogorov-Weiner filter

Grading
Homework assignments.

• J.M. Keynes: " To convert a model into a quantitative formula is to destroy its usefulness as an instrument of thought.
• John Kenneth Galbraith: All financial innovation involves the creation of debt secured in greater or lesser adequacy by real assets. All crises have involved debt that, in one fashion or another, has become dangerously out of scale in relation to the underlying means of payment.