Investment under Risk and Uncertainty 7.5 credits

About the course

This course covers the mathematical and financial theory underpinning capital investments by firms. The course starts with simple investment rules, such as the net present value rule or internal rate of return rule, and then provide a formal discussion of risk aversion, utility theory, stochastic dominance, and related concepts. Following this, the Capital Asset Pricing Model (CAPM) is derived. The course then moves from static to dynamic models, initially in discrete time and then in continuous time. In terms of methodology, the dynamic programming principle and value function iteration are the main focus. From this the real option approach is developed, which extends the net present value rule to cope effectively with features such as flexibility, timing and irreversibility, linking capital investment to the valuation of options. Numerous examples from natural resources, economics, and finance will be explored. Finally, the question of how financing (equity or debt) affects the investment process and the value of the firm, is investigated. This part sets off from the classical Modigliani-Miller theorem, but is extended within a dynamic real options context that accounts for strategic default and allows for determining an optimal capital structure.

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Spring 2027
- Investment under Risk and Uncertainty
  
  Second admissions round for EU/EEA citizens
  
  VT27 / Umeå / English / On site
  
  Application opens 15 September 2026
  
  Save education at universityadmissions.se
  
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  Starts
  18 January 2027
  
  Ends
  24 March 2027
  
  Number of credits
  7.5 credits
  
  Type of studies
  On site
  
  Study pace
  50%
  
  Teaching hours
  Daytime
  
  Study location
  Umeå
  
  Language
  English
  
  Application code
  UMU-5800A
  
  Eligibility
  
  The course requires at least 90 ECTS, including 30 ECTS in Mathematics, at least 15 ECTS in Mathematical Statistics or Statistics, and at least 7,5 ECTS in Programming Methodology, or equivalent. Proficiency in English equivalent to the level required for basic eligibility for higher studies. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.
  
  Selection
  
  Guaranteed place.
  
  Application
  The online application opens 15 September 2026 at 09:00 CET. Application deadline is 15 October 2026. Please note: This second application round is intended only for EU/EEA/Swiss citizens.
  
  Application and tuition fees
  As a citizen of a country outside the European Union (EU), the European Economic Area (EEA) or Switzerland, you are required to pay application and tuition fees for studies at Umeå University.
  
  Application fee: SEK 900
  
  Tuition fee, first instalment: SEK 19,038
  
  Total fee: SEK 19,038
  
  Details about tuition, fees and funding

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