Investment under Risk and Uncertainty

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.