Numerical approximation of a cash-constrained firm value with investment opportunities

Pierre, Erwan, Villeneuve, Stéphane and Warin, Xavier (2017) Numerical approximation of a cash-constrained firm value with investment opportunities. SIAM Journal on Financial Mathematics, 8 (1). pp. 54-81.

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Official URL: http://tse-fr.eu/pub/31157

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: Article
Language: English
Date: 2017
Refereed: Yes
Uncontrolled Keywords: Investment, dividend policy, singular control, viscosity solution, nonlinear PDE
JEL codes: 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)
Site: UT1
Date Deposited: 14 Nov 2016 15:40
Last Modified: 15 Nov 2018 10:30
OAI ID: oai:tse-fr.eu:31157
URI: http://publications.ut-capitole.fr/id/eprint/22492

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