Week 7

Question 1

DO NOT

Answer 1

Differentiate stochastic processes (automatic zero)

Question 2

Exam will definitely have

Answer 2

At least one question relating to ito’s formula

Question 3

Stochastic process X is said to be a Markov Process if

Answer 3

(Markovian ~ have Markov property)

That is to say the future value of X is independent of the past but dependent on the present

Question 4

Relate SDE to Markov property

Answer 4

Any stochastic process which satisfies an SDE has the Markov property

Question 5

Define the multidimensional Ito’s formula

Answer 5

Question 6

Form of SDE from now on

Answer 6

Question 7

Feynman Kac formula (v1)

Answer 7

Question 8

Feynman Kac formula v2

Answer 8

Question 9

Difference between Markov property and Martingale property

Answer 9

Martingale concerns expected value given entire history

Markov is only concerned with current state

Question 10

What does FK formula do

Answer 10

For an Xt that satisfies an SDE (and therefore is markovian)

We can find a function g that we plug the process Xt into to get a conditional expectation