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arXiv · 2206.11534

The maximality principle in singular control with absorption and its applications to the dividend problem

Tiziano De Angelis·Erik Ekström·Marcus Olofsson
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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 2-dimensional 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 non-linear ordinary differential equation. Contrarily to the classical 1-dimensional formulation of the dividend problem, our framework produces a non-trivial solution when the firm's (pre-dividend) equity capital evolves as a geometric Brownian motion. Such solution is also qualitatively different from the one traditionally obtained for the arithmetic Brownian motion.

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Tiziano De Angelis, Erik Ekström, Marcus Olofsson. 2022-06-23. The maximality principle in singular control with absorption and its applications to the dividend problem. https://arxiv.org/abs/2206.11534

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