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Pierre, Erwan, Villeneuve, Stéphane
and Warin, Xavier
(2016)
Numerical approximation of a cash-constrained firm value with investment opportunities.
TSE Working Paper, n. 16-637, Toulouse
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Abstract
We consider a singular control problem with regime switching that arises in problems of optimal investment decisions of cash-constrained firms. The value function is proved to be the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. Moreover, we give regularity properties of the value function as well as a description of the shape of the control regions. Based on these theoretical results, a numerical deterministic approximation of the related HJB variational inequality is provided. We finally show that this numerical approximation converges to the value function. This allows us to describe the investment and dividend optimal policies.
| Item Type: | Monograph (Working Paper) |
|---|---|
| Language: | English |
| Date: | March 2016 |
| Place of Publication: | Toulouse |
| Uncontrolled Keywords: | Investment, dividend policy, singular control, viscosity solution, nonlinear PDE |
| JEL Classification: | C61 - Optimization Techniques; Programming Models; Dynamic Analysis C62 - Existence and Stability Conditions of Equilibrium G35 - Payout Policy |
| Subjects: | B- ECONOMIE ET FINANCE |
| Divisions: | TSE-R (Toulouse), TSM Research (Toulouse) |
| Institution: | Université Toulouse 1 Capitole |
| Site: | UT1 |
| Date Deposited: | 06 May 2016 13:40 |
| Last Modified: | 02 Apr 2021 15:52 |
| OAI Identifier: | oai:tse-fr.eu:30394 |
| URI: | https://publications.ut-capitole.fr/id/eprint/20815 |
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