Mathematics of finance. Options and risks, probability, guarantees and chaos. Tutorial. Shiryaev V.I.

The manual is devoted to the most difficult issues related to the calculation of options depending on the level of a priori uncertainty. A probabilistic, guaranteed approaches to the calculations of options, models of determined chaos, identification of models and their stochastic laws are considered. Possible approaches to a decrease in a priori uncertainty in price evolution models using the R. Kalman filter algorithm, guaranteed assessment algorithms and deterministic chaos models.

, a market model is built for statistically vague situations and a solution to the problem of maintaining the effectiveness of the portfolio on time interval. The models of dynamic chaos are considered.

the manual is intended for students of specialties “Applied Mathematics”, “Applied Mathematics and Informatics”, “Mathematical Methods in the Economics”, and teachers of economic and financial specialties of universities. It will also be useful to students and a wide range of specialists of financial institutions applying financial calculations in their work.