Advances in Applied Probability

The optimal dividend problem in the dual model

Erik Ekström and Bing Lu

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Abstract

We study de Finetti's optimal dividend problem, also known as the optimal harvesting problem, in the dual model. In this model, the firm value is affected both by continuous fluctuations and by upward directed jumps. We use a fixed point method to show that the solution of the optimal dividend problem with jumps can be obtained as the limit of a sequence of stochastic control problems for a diffusion. In each problem, the optimal dividend strategy is of barrier type, and the rate of convergence of the barrier and the corresponding value function is exponential.

Article information

Source
Adv. in Appl. Probab. Volume 46, Number 3 (2014), 746-765.

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1409319558

Digital Object Identifier
doi:10.1239/aap/1409319558

Mathematical Reviews number (MathSciNet)
MR3254340

Zentralblatt MATH identifier
1303.91187

Subjects
Primary: 93E20: Optimal stochastic control
Secondary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 60G51: Processes with independent increments; Lévy processes

Keywords
Optimal distribution of dividends de Finetti's dividend problem optimal harvesting singular stochastic control jump diffusion model

Citation

Ekström, Erik; Lu, Bing. The optimal dividend problem in the dual model. Adv. in Appl. Probab. 46 (2014), no. 3, 746--765. doi:10.1239/aap/1409319558. https://projecteuclid.org/euclid.aap/1409319558


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