Numerical approximation of a cash-constrained firm value with investment opportunities. (English) Zbl 1355.91082
Summary: 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.
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 90B05 | Inventory, storage, reservoirs |
| 91G50 | Corporate finance (dividends, real options, etc.) |
| 49J40 | Variational inequalities |
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