Module Handbook

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Module MAT-61-15-M-7

Continuous-time Portfolio Optimization (M, 4.5 LP)

Module Identification

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 [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Livecycle-State [NORM] Active


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-61-15-K-7
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.


  • 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.

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)


Requirements for attendance (formal)


References to Module / Module Number [MAT-61-15-M-7]

Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)