An Optimal Dividend and Investment Control Problem under Debt Constraints

Etienne Chevalier (1) , Vathana Ly Vath (1) , Simone Scotti (2)

1 LAP - Laboratoire Analyse et Probabilités
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

This paper concerns with the problem of determining an optimal control on the dividend and investment policy of a firm. We allow the company to make an investment by increasing its outstanding indebtedness, which would impact its capital structure and risk profile, thus resulting in higher interest rate debts. We formulate this problem as a mixed singular and switching control problem and use a viscosity solution approach combined with the smooth-fit property to get qualitative descriptions of the solution. We further enrich our studies with a complete resolution of the problem in the two-regime case.

Mots clés: optimal singular; switching problem; debt constraints; stochastic control; viscosity solution; smooth-fit property; system of variational inequalities; debt constraints.

Domaines: Probabilités [math.PR]

Etienne Chevalier, Vathana Ly Vath, Simone Scotti. An Optimal Dividend and Investment Control Problem under Debt Constraints. 2011. ⟨hal-00653293⟩