Irreversible Investment under LLvy Uncertainty: An Equation for the Optimal Boundary

2014 ◽  
Author(s):  
Giorgio Ferrari ◽  
Paavo Salminen
Keyword(s):  
Irreversible Investment ◽  
Optimal Boundary

scholarly journals Irreversible investment under Lévy uncertainty: an equation for the optimal boundary

2016 ◽  
Vol 48 (1) ◽  
pp. 298-314 ◽  
Author(s):  
Giorgio Ferrari ◽  
Paavo Salminen
Keyword(s):  
Integral Equation ◽  
Optimal Investment ◽  
Positive Probability ◽  
Singular Stochastic Control ◽  
Irreversible Investment ◽  
Infinite Time ◽  
Optimal Boundary ◽  
For Profit ◽  
Profit Functions ◽  
New Equation

AbstractWe derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently obtained in a diffusive setting, we show that the optimal boundary is intimately linked to the unique optional solution of an appropriate Bank–El Karoui representation problem. Such a relation and the Wiener–Hopf factorization allow us to derive an integral equation for the optimal investment boundary. In case the underlying Lévy process hits any point inRwith positive probability we show that the integral equation for the investment boundary is uniquely satisfied by the unique solution of another equation which is easier to handle. As a remarkable by-product we prove the continuity of the optimal investment boundary. The paper is concluded with explicit results for profit functions of Cobb–Douglas type and CES type. In the former case the function is separable and in the latter case nonseparable.

scholarly journals Optimal Boundary Surface for Irreversible Investment with Stochastic Costs

2017 ◽  
Vol 42 (4) ◽  
pp. 1135-1161 ◽  
Author(s):  
Tiziano De Angelis ◽  
Salvatore Federico ◽  
Giorgio Ferrari
Keyword(s):  
Boundary Surface ◽  
Irreversible Investment ◽  
Optimal Boundary

Transition to Clean Capital, Irreversible Investment and Stranded Assets

2014 ◽  
Author(s):  
Julie Rozenberg ◽  
Adrien Vogt-Schilb ◽  
Stephane Hallegatte
Keyword(s):  
Irreversible Investment
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