The Annals of Applied Probability

The dividend problem with a finite horizon

Tiziano De Angelis and Erik Ekström

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

Received: September 2016
Revised: January 2017
First available in Project Euclid: 15 December 2017

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Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 93E20: Optimal stochastic control

The dividend problem singular control optimal stopping


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.

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