Module Handbook

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Course MAT-61-15-K-7

Continuous-time Portfolio Optimization (2V, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Additional informations
Livecycle-State [NORM] Active


Each winter semester at least one of the following courses will be offered:[MAT-61-15-K-7], [MAT-61-20-K-7], [MAT-61-30-K-7] or [MAT-61-31-K-7].

The lecture offer for the specialization module planned for the following three semesters will be made available on the website of the master's programme "Actuarial and Financial Mathematics".


  • 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 Course [MAT-61-15-K-7]

Module Name Context
[MAT-61-12A-M-7] Specialization Actuarial and Financial Mathematics WP: Obligation to choose in Obligation to choose-Modulteil #B 2V, 4.5 LP
[MAT-61-15-M-7] Continuous-time Portfolio Optimization P: Obligatory 2V, 4.5 LP