Stochastic Processes in Finance  I
Lecture notes: Week 9 and 10
Professor Shijie Deng
Recall the definition of Conditional Expectation
Discrete r.v. Continuous r.v.
[X  Y = y] = Xi (X = xi  Y = y)
i
[X  Y = y ] =

xf (X  Y = y)dx
Law of Iterative
Stochastic Processes in Finance  I
Lecture notes: Week 7 and 8
Professor Shijie Deng
Dynamically Complete Markets
n
Question: how about another option: say put option with $90, or with arbitrary time2 payoff ( F1 F2 F3 F4 ) Another approach: applying ri
Stochastic Process in Finance  I
Lecture note: Week 5 and 6
Professor: Shijie Deng
ISyE / Math 6759: Stochastic Processes in Finance I
Remember the Big Picture
Representation of o Asset Prices o States of the world o Payoff Matrix o Portfolio Definition
Stochastic processes in Finance  I p
Lecture notes: weeks 3 and 4
Professor Shijie Deng
1
Examples of Conditional Probability
Example 1. E l 1
A prisoner is brought to be in front of 3 doors, behind which, two have lions and one has a princess. The priso
ISyE/Math 6759 y / Stochastic processes in Finance  I
Week 1 & 2 Professor Shijie Deng
Course Topics p
Basic probability theory, conditional expectations p Introduction to basic stochastic processes
1. 2. 3. 4. 5.
Poisson Process Markov h i M k chains e.