```
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,

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.

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. |

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.

**email:**

md1ahlda(a)math.chalmers.se**www:**

http://www.math.chalmers.se/~md1ahlda**Telephone:**031 - 772 5379**Room:**MVL:3070**Adress:**Matematisk Statistik, CTH & GU, 412 96 Göteborg, Sweden