Investment under Risk and Uncertainty

Education facts

Code: 5MA218

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.

Entry requirements

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.

Education offerings

Each offering has its own dates and conditions. Closed offerings are retained as history and do not mean that a new application is open.

• Investment under Risk and Uncertainty

  Umeå University

  Start date: 18 January 2027

  End date: 24 March 2027

  Pace of study: 50 %