An irreversible investment problem with demand on a finite horizon: The optimal investment boundary analysis

This paper studies a continuous-time, finite horizon, irreversible investment problem where a social planner aims to minimize total expected costs of production capacity and demand. Our model allows for general diffusion dynamics on the demand as well as production capacity process controlled by a n...

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Vydané v:Communications in nonlinear science & numerical simulation Ročník 109; s. 106302
Hlavní autori: Han, Xiaoru, Yi, Fahuai
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.06.2022
Elsevier Science Ltd
Predmet:
Boundary conditions
Demand
Finite element analysis
Finite horizon
Free boundaries
Horizon
Investment
Irreversible investment
Optimal control
Optimal investment boundary
Partial differential equations
Singular stochastic control
Stochastic models
Stochastic processes
Finite horizon
Optimal investment boundary
Irreversible investment
Singular stochastic control
ISSN:1007-5704, 1878-7274
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Shrnutí:This paper studies a continuous-time, finite horizon, irreversible investment problem where a social planner aims to minimize total expected costs of production capacity and demand. Our model allows for general diffusion dynamics on the demand as well as production capacity process controlled by a nondecreasing process representing the cumulative investment. Mathematically, it is a singular stochastic control problem whose value function satisfies a two-dimensional parabolic variational inequality with gradient constraint. The problem gives rise to a free boundary which stands for the optimal investment boundary. We use partial differential equation (PDE) approach to characterize some features of the free boundary and prove the C2,1 regularity of the value function. To the best of our knowledge, the method to study the monotonicity of free boundary about the time direction is an innovation. •Study optimal irreversible investment problem on finite horizon.•Characterize continuity, monotonicity and asymptote of optimal investment boundary.•Method to study monotonicity of free boundary about time is an innovation.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2022.106302