Exercises and hand-ins 2007

TMS165/MSN600 Stochastic Calculus, Part I, 5 credits (Stokastisk analys, del I, 5 poäng)


The hand-in exercises are, respectively, due to fridays during the remainings of this course. Students are recomended to hand in the assignments two and two. They may be handed in during class, or to me at room MVL:3070. Solutions should be well motivated, clear and easy to read. Especially should simulations be explained carefully. The grades for this course will be based on your solutions of the hand-in problems.

Grading: To pass this course, we will implement the following algorithm:
  function G=pass(X)            % G=1 means pass, G=0 fail, X vector with hand-in scores
  M=[M1, M2, M3, M4, M5, M6];   % maximum on each hand-in
  S=sum(X);                     % total points
  for i=1:6
    if X(i)<0.3*M(i)
  if S< 0.5*sum(M)

That is, 50% of the total score must be achived, and at least 30% on each hand-in. Note: Simulations are a part of this course that cannot be neglected. Understanding this algorithm is a good start!

Deadline: All hand-ins must be handed in by October 26! Students who fail to do so, we cannot promise when their grades will be available for registration in the Ladok-system.

No 1. Due September 14.
No 2. Due September 21.
No 3. Due October 5.
No 4. Due October 12. Simulation to problem 2 may look like this. Also, I have one hand-in 4 without namo on. Please come by and identify it if you haven't had yours back! (good grade)
No 5. Due October 19.
No 6. Due October 26.
ps-file, pdf-file.

Exercise sessions

For students not able to join exercise sections, short solutions are avalible for some of the problems.
No 1. September 7 ps-file, pdf-file. Solutions ps-file, pdf-file.
No 2. September 14 ps-file, pdf-file.
No 3. September 21 ps-file, pdf-file. Solutions ps-file, pdf-file.
No 4. September 28 ps-file, pdf-file. Solutions ps-file, pdf-file.
No 5. October 5. Exercises 4.1,7,9,18 and 5.1,3 in Klebaner.
No 6. October 10, Wednesday! ps-file, pdf-file. We look at examples of an SDE with stationary distribution (Ornstein-Uhlenbeck) and one without (Black-Scholes). The Matlab simulations can be found here: Ornstein-Uhlenbeck, pictures 1, 2, 3. Black-Scholes, pictures 1, 2.

Some additional reading, by Anders Muszta

Probability Basics (pdf)
Probability Basics (postscript)

Browninan Quadratic variation (pdf)
Browninan Quadratic variation (postscript)

Solving SDE (pdf)
Solving SDE (ps)

Stochastic integral process (pdf)
Stochastic integral process (postscript)

Stochastic integral random variable (pdf)
Stochastic integral random variable (postscript)

Ito formula (pdf)
Ito formula (postscript)

Solving advanced SDE (pdf)
Solving advanced SDE (postscript)

Course Programme ps-file, pdf-file, dvi-file.

Daniel Ahlberg is responsible for exercises and hand-ins. If you have any doubts or questions, you are welcome to contact me.

Telephone: 031 - 772 5379
Room: MVL:3070
Adress: Matematisk Statistik, CTH & GU, 412 96 Göteborg, Sweden