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Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs

Part of: Existence theories Stochastic systems and control Markov processes Optimality conditions

Published online by Cambridge University Press:  01 July 2016

Jostein Paulsen
Jostein Paulsen*
Affiliation:
University of Bergen
*
∗ Postal address: Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, 5008 Bergen, Norway. Email address: jostein@mi.uib.no
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Abstract

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The problem of optimal dividends paid until absorbtion at zero is considered for a rather general diffusion model. With each dividend payment there is a proportional cost and a fixed cost. It is shown that there can be essentially three different solutions depending on the model parameters and the costs. (i) Whenever assets reach a barrier y*, they are reduced to y* - δ* through a dividend payment, and the process continues. (ii) Whenever assets reach a barrier y*, everything is paid out as dividends and the process terminates. (iii) There is no optimal policy, but the value function is approximated by policies of one of the two above forms for increasing barriers. A method to numerically find the optimal policy (if it exists) is presented and numerical examples are given.

Keywords

Optimal dividenddiffusion modelimpulse controlbarrier strategy

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 49J15: Optimal control problems involving ordinary differential equations 49K15: Problems involving ordinary differential equations 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 3 , September 2007 , pp. 669 - 689
Copyright
Copyright © Applied Probability Trust 2007 

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