Stopping Time Problems In Economics

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• 研討會日期 : 2016-03-17
• 時間 : 14:00
• 主講人 : Professor Svetlana Boyarchenko
• 主持人 : Professor Yu-Chin Hsu
• 地點 : Conference Room B110
• 演講者簡介 : Professor Boyarchenko received her Ph.D. in Economics from University of Pennsylvania, Philadelphia, U.S.A. in 2001. She is currently an Associate Professor at University of Texas at Austin. Her current research interests are efficient option pricing methods, optimal stopping problems under risk and uncertainty, stopping time games and experimentation and learning models.
• 演講摘要 : Optimal timing of actions is an essential part of decision making. Examples include, but are not limited to, pricing of derivatives, real investment opportunities or insurance contracts, entry into a new market, capital accumulation, product or project innovations, default on household or sovereign debt, exit from a declining industry, quitting an old job and accepting a new offer, natural resource extraction. My lectures will give an introduction to optimal timing of irreversible or costly reversible actions in a risky environment. I will focus on a well-developed approach to this kind of problems which is called the Real Options approach, due to the fact that it essentially uses the valuation technique of American type derivatives. ※ Outline: The first lecture will introduce the building blocks of the Real Options approach. To explain the main idea of the option value of waiting, I will use discrete state and 2-3 period discrete time models. The examples include timing fixed size investment in a risky project, exit from a declining industry, and investment with and embedded option of exit. Then, I will extend basic real options situations for infinite time horizon (perpetual real options) and uncertainty modeled as stochastic processes with independent increments (random walks in discrete time, and Levy processes in continuous time). This lecture will be based on the following papers 1. S. Boyarchenko and S. Levendorskii, ‘’Optimal stopping made easy," Journal of Mathematical Economics, 43:2 (2007), pp. 201-217 2. S. Boyarchenko and S. Levendorskii, “Practical guide to real options in discrete time," International Economic Review, 48:1 (2007), pp. 311-342 3. S. Boyarchenko, “Irreversible decisions and record setting news principles," American Economic Review, 94:3 (2004), pp. 557-568 4. S. Boyarchenko and S. Levendorskii, “General option exercise rules, with applications to embedded options and monopolistic expansion," Contributions to Theoretical Economics, 6:1, article 2 (2006) The second lecture will be focused on the following applications of the optimal stopping theory: (i). Stopping time games and real options: this application shows how competition and different kinds of risk affect real investment decisions. The model example deals with the case of two investors into a new market. There is a tradeoff between moving first and exploiting the first mover's advantage and waiting for more information about the state of the market. (ii). Optimal stopping decisions under Knightian uncertainty. The aim of this model is to explain differences between decision making in a single prior and multiple priors models and determine the optimal investment strategy in a multiple priors model. The necessity of multiple priors models is evident, for example, in case of truly innovative breakthroughs, where information about future profitability of a project is too imprecise to be described adequately by a single probability prior. Also, insurance companies may base their contracts on several probability distributions of a certain disaster as assessed by different specialists in the area. (iii). Random observations. This model bridges together the classical real investment or disinvestment models with the so called exponential bandits models, where the investor observes the information about the revenue or cost process at random times. I will present two leading examples: one is an insurance company that observes costly accidents that happen at random and has to decide when to terminate a contract. The other example is a venture capitalist that has to decide when to invest into a startup whose protable breakthroughs happen at random times. This lecture will be based on the following papers 5. S. Boyarchenko and S. Levendorskii, “Preemption Games under Levy Uncertainty," Games and Economic Behavior, 88 (2014), pp. 354-380 6. S. Boyarchenko and S. Levendorskii, “Ambiguous jump-diffusions and optimal stopping," Working paper available at http://ssrn.com/abstract=2514032 7. S. Boyarchenko and S. Levendorskii, “Poisson Bandits of Evolving Shade of Gray," Working paper available at https://www.dropbox.com/s/1j5a6m2fkbk3g8q/GreyBandit11a.pdf?dl=0