Robust Irreversible Investment
DFG-Projekt Ri 1128-3-1
Abstract Publications/Talks Participants News/Jobs Institutions/Literature
Publications
Riedel, F. (2007): Optimal Stopping under Ambiguity.Abstract: We consider optimal stopping problems for ambiguity averse decision makers with multiple priors. In general, backward induction fails. If, however, the class of priors is time–consistent, we establish a gen- eralization of the classical theory of optimal stopping. To this end, we develop first steps of a martingale theory for multiple priors. We define minimax (super)martingales, provide a Doob–Meyer decompo- sition, and characterize minimax martingales. This allows us to ex- tend the standard backward induction procedure to ambiguous, time– consistent preferences. The value function is the smallest process that is a minimax supermartingale and dominates the payoff process. It is optimal to stop when the current payoff is equal to the value function. Moving on, we study the infinite horizon case. We show that the value process satisfies the same backward recursion (Bellman equation) as in the finite horizon case. The finite horizon solutions converge to the infinite horizon solution. Finally, we characterize completely the set of time–consistent multiple priors in the binomial tree. We solve two classes of examples: the so–called independent and indistinguish- able case (the parking problem) and the case of American Options (Cox–Ross–Rubinstein model).
Key words and phrases: Optimal Stopping, Ambiguity, Uncertainty AversionJEL subject classification: D81, C61, G11
Paper available online
Paulsen, D. (2006): Stochastic Oligopoly Games under Irreversibility, Diplomarbeit.
Paper available online
Su, X. & Riedel, F. (2006): On Irreversible Investment.
Abstract: This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first contribution, a general existence and uniqueness result is provided for the optimal investment policy. Based upon an alternative approach developed previously to dynamic programming problems, we derive the optimal base capacity policy such that the firm always keeps the capacity at or above the base capacity. The critical base capacity is explicitly constructed and characterized via a stochastic backward equation. This method allows qualitative insights into the nature of the optimal investment under irreversibility. Finally, explicit solutions are derived for infinite time horizon, a separable operating profit function of Cobb-Douglas type and an exponential Lévy process modelled economic shock.
Key words and phrases: Sequential Irreversible Investment, Capacity Expansion, Singular Control Problem, Lévy Processes.JEL subject classification: C61, D81, E22, G11
Paper available online
Schroeder, D. (2006): Investment under Ambiguity With the Best and Worst in Mind.
Abstract: Recent literature on optimal investment has stressed the difference between the impact of risk compared to ambiguity - also called Knightian uncertainty - on investors’ decisions. However, the decision maker’s attitude towards ambiguity is crucial when analyzing his investment decisions given an uncertain environment. By introducing an individual parameter reflecting personal characteristics of the entrepreneur, our simple irreversible investment model helps to explain differences in investment behavior in situations which are objectively identical. This paper shows that the presence of ambiguity leads in many cases to an increase in the subjective project value, and entrepreneurs are more eager to invest.
Paper available online
Talks/Participation
Coming up:Past:
Wissenschaftszentrum Berlin (WZB), Microeconomics Seminar
October 30th, 2006
13th Annual Meeting of the German Finance Association (DGF)
October 6th-7th, 2006
61st European Meeting of the Econometric Society
August 24th-28th, 2006
Fourth World Congress of the Bachelier Finance Society
August 17th-20th, 2006
Real Options. Tenth Annual International Conference
June 14th-17th, 2006
Cornell University, Financial Engineering Seminar
March 2nd, 2006
Princeton University, Operation Research and Financial Engineering Seminar
February 28th, 2006
University of Bonn, Department of Mathematics
February 9th, 2006
Ruprecht-Karls University Heidelberg, Department of Economics and Social Sciences
December 12th, 2005
Swiss Federal Institute of Technology Zürich, Department of Mathematics
January 27th, 2005