## Annals of Applied Probability

### The dividend problem with a finite horizon

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 27, Number 6 (2017), 3525-3546.

Dates
Revised: January 2017
First available in Project Euclid: 15 December 2017

https://projecteuclid.org/euclid.aoap/1513328707

Digital Object Identifier
doi:10.1214/17-AAP1286

Mathematical Reviews number (MathSciNet)
MR3737931

Zentralblatt MATH identifier
06848272

#### Citation

De Angelis, Tiziano; Ekström, Erik. The dividend problem with a finite horizon. Ann. Appl. Probab. 27 (2017), no. 6, 3525--3546. doi:10.1214/17-AAP1286. https://projecteuclid.org/euclid.aoap/1513328707

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