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# TMS165/MSA350 Stochastic Calculus Part I, 2008, Hand-ins and Exercises

Johan Tykesson is responsible for the hand-ins and exercises.

## Hand-ins

Here are the hand-ins: ps-file, pdf-file.

The hand-ins are due on fridays according to the following schedule:

No 1. Due September 19.
No 2. Due September 26.
No 3. Due October 10.
No 4. Due October 17. Simulation to problem 2 may look like this.
No 5. Due October 24.
No 6. Due October 31.

Deadline: All hand-ins must be handed in by October 31! Students who fail to do so, we cannot promise when their grades will be available for registration in the Ladok-system.

Students are recomended to work with the hand-ins in pairs. The hand-ins may be handed in during classes or to Johan in room MVL:3088 (there are boxes for hand-ins outside Johans door, should he not be in). Solutions should be well motivated, clear and easy to read. Especially should simulations be explained carefully. The grades for the course will be based on the quality of the hand-ins.

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   G=1;   for i=1:6     if X(i)<0.3*M(i)       G=0;     end   end   if S< 0.5*sum(M)      G=0;   end ```
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!

## Exercise sessions

For students not able to join exercise sections, short solutions are avalible for some of the problems.
 No 1. September 12 ps-file, pdf-file. Solutions ps-file, pdf-file. No 2. September 19 ps-file, pdf-file. No 3. September 26 ps-file, pdf-file. Solutions ps-file, pdf-file. No 4. October 3 ps-file, pdf-file. Solutions ps-file, pdf-file. No 5. October 10. Exercises 4.1,7,9,18 and 5.1,3 in Klebaner. No 6. October 17 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.