NMAA09045U Finance 2: Dynamic Portfolio Choice (Fin2)

Volume 2024/2025

MSc Programme in Mathematics-Economics


See the "Knowledge" part of the learning outcome below.

Learning Outcome


  • A closer look at arbitrages: No arbitrage-intervals in incomplete markets, cross-currency betting arbitrage, statistical arbitrage.
  • Maximization of expected utility and (partial) equilibrium in one-period models, the state-price utility theorem and betting against beta.
  • Multi-period optimal portfolio choice. The martingale method vs. dynamic programming/the Bellman equation.
  • Explicit solutions in binomial(‘ish) models and in amodel with reurn preditability and transaction costs. 
  • Properties and consequences of solutions; myopia and constant weights, C-CAPM, the equity premium puzzle.
  • The numeraire porttfolio.
  • Optimal stopping and the hedging and pricing of American options including Longstaff and Schwartz' simulation technique.



  • Rigorously prove optimality principles and conditions for stochastic control problems in (discrete time, finite space)-multi-period setting.
  • Explicitly solve simple investment/consumption and optimal stopping problems.   
  • Derive (with pen and paper), analyze (with a computer) and explain (in plain English) model implications; be they quantitative or qualitative, be they regarding policy, equilibrium, or empirics.



  • Formulate and analyze decision problems (investment/consumption and optimal stopping) in a stochastic multi-period setting.
  • Analyze model consequences “with numbers”; algorithmically, experimentally or empirically. (As well as understand why these three things are different concepts.)
  • Acquire the confidence to read presentations of the same - or almost the same - problem in the literature. Know that notation, motivation, and rigour varies and that there is rarely a gospel.
A bachelor degree in Mathematics-Economics.

Academic qualifications equivalent to a BSc degree is recommended.
Blended teaching and learning: 4 hours of video lectures per week for 7 weeks. Worksheets with exercises/problem solving will be provided for the students for in-depth engagement with the course material. There will be regular meetings with the lecturer for discussions of the course material and the exam.
This course is only available to students enrolled in the MSc Programme in Mathematics-Economics in the study year 2023/24 and earlier.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 177
  • Exam
  • 1
  • Total
  • 206
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Oral examination, 20 minutes (no prepartion)
Type of assessment details
Without preparation time, but "open book" (i.e. "all aids allowed").
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship

Same as ordinary

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.