Finance 2: Dynamic Portfolio Choice (Fin2)

Course content

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


MSc Programme in Mathematics-Economics

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.

4 hours of lectures and 2 hours of tutorials per week for 7 weeks.

A bachelor degree in Mathematics-Economics.

Academic qualifications equivalent to a BSc degree is recommended.

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 assessment

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

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 163
  • Theory exercises
  • 14
  • Exam
  • 1
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 4
No limit
The number of seats may be reduced in the late registration period
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Rolf Poulsen   (4-83807d77517e7285793f7c863f757c)
Office, 04.4.11
Saved on the 28-02-2023

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