The dividend problem with a finite horizon

Tiziano De Angelis; Erik Ekström

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arXiv · 1609.01655

The dividend problem with a finite horizon

Tiziano De Angelis·Erik Ekström

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Abstract

We characterise the value function of the optimal dividend problem with a finite time horizon as the unique classical solution of a suitable Hamilton-Jacobi-Bellman equation. The optimal dividend strategy is realised by a Skorokhod reflection of the fund's value at a time-dependent optimal boundary. Our results are obtained by establishing for the first time a new connection between singular control problems with an absorbing boundary and optimal stopping problems on a diffusion reflected at $0$ and created at a rate proportional to its local time.

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Tiziano De Angelis, Erik Ekström. 2016-09-06. The dividend problem with a finite horizon. https://arxiv.org/abs/1609.01655

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