With the given theories and tools the student needs:
- To be able to write a paper on a self chosen recent academic publication in the field of investment under uncertainty (real options).
- To be able to solve a real options problem.
- To be able to solve deterministic dynamic models of the firm.
- To have developed economic intuition concerning dynamic capital investments decisions.
The course consists of two parts, which distinguish stochastic and deterministic dynamic optimisation. Part 1 deals with the stochastic part, and the topic is real option theory. For this part the book by Dixit and Pindyck (1996) is treated. It concerns capital investment decisions of firms, stressing the irreversibility of most investment decisions, and the ongoing uncertainty of the economic environment in which these decisions are made. To support this kind of decision making several mathematical tools are introduced such as dynamic programming and stochastic processes like Brownian motion and Poisson processes. The Dixit-Pindyck book mainly considers single decision maker problems of firms operating in monopoly or perfect competition markets. In the course we will also deal with the problem of investment timing in an oligopoly framework. This requires a merge between game theory and real options. The examination of this part partly consists of writing a paper.Part 2 deals with optimisation techniques for deterministic dynamic systems, which are applied to dynamic models of the firm. The emphasis lies on the economic interpretation of the mathematical optimisation results. The topics are: Pontryagin's maximum principle, applications to dynamic models of the firm, effects of environmental regulation on the firm's dynamic investment behaviour. The written exam consists of Part 1 (30%) and Part 2 (70%).
Type of instructions
3 contact hours a week
Type of exams
writing a paper (0.5) plus written exam (0.5)
- A.K. Dixit, R.S. Pindyck, Investment under Uncertainty, Princeton University Press, Princeton, second printing, 1996.
- P.M. Kort, J.M. Schumacher, Course Notes on Dynamic Optimization (Part 1+2).
- Recent papers from various journals
- P.M. Kort, Real Options Basic Theory, 2018.
- P.M. Kort, Real Options Capacity Size, 2018.
- G. Feichtinger and R.F. Hartl, Optimale Kontrolle Oekonomischer Prozesse, Anwendungen des Maximumprinzips in den Wirtschafswissenschaften, De Gruyter, Berlijn, 1986.
- O. van Hilten, P.M. Kort and P.J.J.M. van Loon, Dynamic Policies of Firm: An Optimal Control Approach, Springer, Berlijn, 1993.
- A. Seierstad and K. Sydsaeter, Optimal Control Theory with Economic Applications, North-Holland, Amsterdam, 1987.