NMAA09045U Finance 2: Dynamic Portfolio Choice (Fin2)

Volume 2022/2023

MSc Programme in Mathematics-Economics


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

Learning Outcome


  1. Formulate and analyze decision problems (investment/consumption and optimal stopping) in a stochastic multi-period setting.
  2. Analyze model consequences “with numbers”; algorithmically, experimentally or empirically. (As well as understand why these three things are different concepts.)
  3. 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.   


  • 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.


  • 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.
A bachelor degree in Mathematics-Economics.

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lectures and 2 hours of tutorials per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 163
  • Theory exercises
  • 14
  • Exam
  • 1
  • Total
  • 206
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Oral examination, 20 minutes
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 must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.