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Last update: doc. RNDr. Martin Branda, Ph.D. (14.12.2020)
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Last update: RNDr. Jitka Zichová, Dr. (01.06.2022)
The main objective is to introduce the fundamentals of probability theory that are used in finance and insurance mathematics. |
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Last update: prof. RNDr. Bohdan Maslowski, DrSc. (28.09.2023)
The credit for exercise class must be obtained prior to taking the exam.
The credit for exercise class is obtained for personal presence at four (at least) exercise classes (the total number of which is seven). If this condition is not met, it is necessary to submit solutions to assigned exercise in written form. |
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Last update: prof. RNDr. Bohdan Maslowski, DrSc. (14.12.2020)
P. Lachout: Diskrétní martingaly, Lecture Notes MFF UK B. Oksendal: Stochastic Differential Equations, Springer-Verlag, 2010 I. Karatzas and S.E. Shreve: Brownian Motion and Stochastic Calculus, Springer-Verlag, 1988 J. M. Steele, Stochastic Calculus and Financial Applications, Springer-Verlag, 2001 |
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Last update: RNDr. Jitka Zichová, Dr. (01.06.2022)
Lecture + exercises. |
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Last update: prof. RNDr. Bohdan Maslowski, DrSc. (14.12.2020)
1. Conditional expectation w.r.t. sigma-algebra, random process, finite-dimensional distributions, Daniell-Kolmogorov and Kolmogorov-Chentsov theorems.
2. Martingales, definition of super- and submartingales, filtration, basic examples. Stopping times and hitting times of a subset of the state space by a random process. Maximal inequalities, Doob-Meyer decomposition.
3. Quadratic variation of martingales, Wiener process and its basic properties.
4. Stochastic integration w.r.t. Wiener process, definition and basic properties. Stochastic differential and Ito formula, examples.
5. Stochastic integration w.r.t. martingales - an introduction. |