1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2022/2023
4. Mathematics - drugiego stopnia z tyt. magistra
5. Modeling in Finance 2

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Modeling in Finance 2 - opis przedmiotu

Cel przedmiotu

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.

Wymagania wstępne

Zapisz zmiany

Knowledge of fundamental courses in mathematical analysis, probability theory, basic stochastic processes, financial mathematics, mathematical modeling, and numerical methods is required.

Zakres tematyczny

 

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.

Metody kształcenia

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.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

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.

Literatura podstawowa

1. A.N. Shiryaev, Essentials of Stochastic Finance, World Scientific, 1999.
2. T. Rolski et al. Stochastic processes for insurance and finance, Wiley 1999.
3. M. Musiela, M. Rutkowski, Martingale Methods in Financial Modelling, Springer, 1997.
4. J. Grandell, Aspects of Risk Theory, Springer, Berlin,1992.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr hab. Mariusz Michta, prof. UZ (ostatnia modyfikacja: 10-01-2024 19:44)