- Introduction to portfolio optimization (problem statement),
- Continuous-time portfolio problem: expected utility approach,
- Martingale method for complete markets,
- Stochastic control approach (HJB equation, verification theorems),
- Portfolio-Optimization with restrictions (e.g. risk constraints, transaction costs),
- Comparison with mean-variance analysis (Markowitz),
- Portfolio optimization with financial derivatives,
- Alternative methods.
Continuous-time Portfolio Optimization (M, 4.5 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-61-15-M-7||Continuous-time Portfolio Optimization||4.5 CP (135 h)|
|CP, Effort||4.5 CP = 135 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
Lecturers of the department Mathematics
|Area of study||[MAT-STO] Stochastics/Statistics/Financial Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Continuous-time Portfolio Optimization
|P||28 h||107 h||-||-||PL1||4.5||irreg.|
- About [MAT-61-15-K-7]: Title: "Continuous-time Portfolio Optimization"; Presence-Time: 28 h; Self-Study: 107 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 86180 ("Continuous-Time Portfolio Optimization")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
Students know and understand the two main methods for solving stochastic control problems in financial and actuarial mathematics, i.e. the stochastic control approach and the duality approach. They understand the proofs presented in the lecture and are able to reconstruct and explain them. They can apply the methods to various problems of portfolio optimization and critically assess the implementation and application of the theoretical results. They are able to assess the applicability of alternative methods under various model extensions and restrictions to the strategies and understand the impact these have on the optimal solutions.
- I. Karatzas, S.E. Shreve: Methods of Mathematical Finance,
- R. Korn: Optimal Portfolios,
- R. Korn, E. Korn: Option Pricing and Portfolio Optimization - Modern Methods of Financial Mathematics,
- H. Pham: Continuous-time Stochastic Control and Optimization with Financial Applications.
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-61-11-M-7] Financial Mathematics (M, 9.0 LP)
Requirements for attendance (formal)