OPTIMIZATION PROBLEMS IN

STATISTICS AND FINANCIAL

MATHEMATICS

05–16.03.2001, Tampere

Unit 1. Optimization : 3 hours Basic Notions and Facts.

Unit 2. Statistics : 7 hours Optimal Linear Unbiased Estimators for Location and Scale Parameters. Maximum Likelihood Estimators. Linear Regression Model. Least Squares Estimators. Best Linear Unbiased Estimators. Optimal Confidence Set. Optimal Confidence Interval for Regression Function at a Given Point.

Unit 3. Financial Mathematics : 7 hours Binary Model. Options. Optimal Capital Evolution and Fair Price. Option Quality. Optimal Options. Optimal Stock Portfolio.

Unit 4. Exercises : 3 hours

Literature

Optimization :

1. Bazaraa, M.S., Shetty, C.M. Nonlinear Programming Theory and Algorithms, John Wiley, New York, 1979.

2. Jeter, M.W. Mathematical Programming, Marcel Dekker, New York, 1986.

3. Mangasarian, O.L. Nonlinear Programming, SIAM, Philadelphia, 1994.

4. Polyak, B.T. Introduction to Optimization, Translation Series in Mathematics and Engineering, New York, 1987. Statistics :

1. Lehmann, E.L. Theory of Point Estimation, John Wiley, New York, 1983.

2. Miller, R.G., Jr Simultaneous Statistical Inference, Springer-Verlag, New York, 1981.

3. Rao, C.R. Linear Statistical Inference and Its Applications, John Wiley, New York, 1973.

4. Silvey, S.D. Statistical Inference, John Wiley, New York, 1975. Financial Mathematics :

1. Karatzas, I., Shreve, S.E. Methods of Mathematical Finance, Springer-Verlag, New York, 1998.

2. Musiela, M., Rutkowski, M. Martingale Methods in Financial Modelling, Springer-Verlag, New York, 1997.

3. Probability Theory and Its Applications, 1994, 39, No 1.