Erwan Pierre, Stéphane Villeneuve, and Xavier Warin, Numerical approximation of a cash-constrained firm value with investment opportunities., IDEI Working Paper, n. 860, March 2016.


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.


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

Research partnership

Électricité de France (EDF)