The Maximality Principle in Singular Control with Absorption and Its Applications to the Dividend Problem
Articolo
Data di Pubblicazione:
2024
Abstract:
Motivated by a new formulation of the classical dividend problem, we show that Peskir's maximality principle can be transferred to singular stochastic control problems with twodimensional degenerate dynamics and absorption along the diagonal of the state space. We construct an optimal control as a Skorokhod reflection along a moving barrier, where the barrier can be computed analytically as the smallest solution to a certain nonlinear ODE. Contrarily to the classical one-dimensional formulation of the dividend problem, our framework produces a nontrivial solution when the firm's (predividend) equity capital evolves as a geometric Brownian motion. Such a solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.
Tipologia CRIS:
03A-Articolo su Rivista
Keywords:
singular control with absorption; maximality principle; dividend problem; optimal stopping; free boundary problems
Elenco autori:
De Angelis, Tiziano; Ekström, Erik; Olofsson, Marcus
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