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The Optimal Dividend Problem in the Dual Model

Part of: Stochastic processes Stochastic systems and control Mathematical finance

Published online by Cambridge University Press:  22 February 2016

Erik Ekström  and
Bing Lu
Erik Ekström*
Affiliation:
Uppsala University
Bing Lu*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
∗ Postal address: Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, Sweden.
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Abstract

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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.

Keywords

Optimal distribution of dividendsde Finetti's dividend problemoptimal harvestingsingular stochastic controljump diffusion model

MSC classification

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; L'evy processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 746 - 765
Copyright
© Applied Probability Trust 

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