2016/03/30 by Erwan Pierre, Stéphane Villeneuve, Pierre, Erwan +3
Economics, Econometrics and Finance · #91G60 #Climate Change Policy and Economics #Computational Finance (q-fin.CP) #Economic theories and models #FOS: Economics and business #Stochastic processes and financial applications #msc:91G60 #q-fin.CP
paper · pdf · doi:10.48550/arxiv.1603.09049
30 pages, 10 figures
openalex publication_date 2016/03/30 · arxiv created 2016/10/06 · arxiv updated 2016/10/07 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
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.