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Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching

Part of: Stochastic systems and control Stochastic analysis Mathematical economics

Published online by Cambridge University Press:  30 January 2018

Zhengjun Jiang
Zhengjun Jiang*
Affiliation:
Beijing Normal University - Hong Kong Baptist University United International College
*
∗ Postal address: Beijing Normal University - Hong Kong Baptist University United International College, 28 Jinfeng Road, Tangjiawan, Zhuhai, 519085, P. R. China. Email address: [email protected]
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Abstract

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In this paper we study the optimal dividend payments for a company of limited liability whose cash reserves in the absence of dividends follow a Markov-modulated jump-diffusion process with positive drifts and negative exponential jumps, where parameters and discount rates are modulated by a finite-state irreducible Markov chain. The main aim is to maximize the expected cumulative discounted dividend payments until bankruptcy time when cash reserves are nonpositive for the first time. We extend the results of Jiang and Pistorius [15] to our setup by proving that it is optimal to adopt a modulated barrier strategy at certain positive regime-dependent levels and that the value function can be explicitly characterized as the fixed point of a contraction.

Keywords

Optimal dividend policyMarkov chainregime switchingjump-diffusion processstochastic control

MSC classification

Primary: 93E20: Optimal stochastic control
Secondary: 91B70: Stochastic models 60H30: Applications of stochastic analysis (to PDE, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 1 , March 2015 , pp. 209 - 223
Copyright
© Applied Probability Trust 

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