A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis
AbstractWe study a continuous-time, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investmentdisinvestment problem a zero-sum optimal stopping game and characterize its value function through a free boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diffusion reflected at the two boundaries.
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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 477.
Length: 42 pages
Date of creation: Apr 2013
Date of revision:
reversible investment; singular stochastic control; zero-sum optimal stopping games; free boundary problems; Skorokhod reflection problem;
Find related papers by JEL classification:
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
- E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity
- D92 - Microeconomics - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-04-20 (All new papers)
- NEP-GTH-2013-04-20 (Game Theory)
- NEP-ORE-2013-04-20 (Operations Research)
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