SylabUZ
Nazwa przedmiotu | Modeling in Finance 2 |
Kod przedmiotu | 11.5-WK-MATED-MF2-S22 |
Wydział | Wydział Matematyki, Informatyki i Ekonometrii |
Kierunek | Mathematics |
Profil | ogólnoakademicki |
Rodzaj studiów | drugiego stopnia z tyt. magistra |
Semestr rozpoczęcia | semestr zimowy 2023/2024 |
Semestr | 3 |
Liczba punktów ECTS do zdobycia | 6 |
Typ przedmiotu | obieralny |
Język nauczania | angielski |
Sylabus opracował |
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Forma zajęć | Liczba godzin w semestrze (stacjonarne) | Liczba godzin w tygodniu (stacjonarne) | Liczba godzin w semestrze (niestacjonarne) | Liczba godzin w tygodniu (niestacjonarne) | Forma zaliczenia |
Wykład | 30 | 2 | - | - | Egzamin |
Laboratorium | 30 | 2 | - | - | Zaliczenie na ocenę |
The course covers topics related to selected methods of mathematical modeling in finance and insurance. The classes aim to familiarize students with the fundamental methods of modeling in financial markets and insurance.
Knowledge of fundamental courses in mathematical analysis, probability theory, basic stochastic processes, financial mathematics, mathematical modeling, and numerical methods is required.
Lecture:
1.Stochastic processes with continuous time – measurability, adaptability, non-anticipating processes, processes with finite variation, martingales, stopping times, local martingales – Wiener and Poisson processes.
2. Lebesgue-Stieltjes integral concept and Ito integral – properties, Ito processes, and Ito's formula.
3. Girsanov's Theorem.
4. Black-Scholes market model and arbitrage theory-equivalent martingale measure.
5. Self-financing strategies and replicating derivative instruments.
6. Martingale valuation of standard European options.
7. Exotic options – basic types and applications.
8. Elements of classical risk theory – insurance reserve model.
9. Basic distributions – Poisson process and compound Poisson process. Interval estimation of the number of insurance claims.
10. Application of martingales for estimating the probability of ruin – Cramér-Lundberg inequality.
11. Probability of ruin estimation for a life insurance policy portfolio.
Laboratory:
1. Options valuation and computer simulation of results in continuous financial models.
2. Visualization of stock market data, basic calculations, and simulations related to stock market data.
Lecture:
The lecture will be enriched with illustrative accounting examples, providing practical insights into the discussed topics.
Laboratory:
The laboratory sessions will involve both individual and group-solving of tasks using real-world data with the aid of computer programs. Each session will begin with a discussion on the theoretical tools required, followed by individual elaborations on the solutions to selected tasks presented in the form of reports.
Opis efektu | Symbole efektów | Metody weryfikacji | Forma zajęć |
The subject assessment is comprised of a laboratory grade (40%) and an examination grade (60%). A prerequisite for taking the exam is a positive laboratory grade. To pass the subject, both a positive laboratory grade and a positive exam grade are required.
Zmodyfikowane przez dr Ewa Sylwestrzak-Maślanka (ostatnia modyfikacja: 10-04-2024 16:08)