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ON THE INTERFACE BETWEEN OPTIMAL PERIODIC AND CONTINUOUS DIVIDEND STRATEGIES IN THE PRESENCE OF TRANSACTION COSTS

Published online by Cambridge University Press:  13 June 2016

Benjamin Avanzi ,
Vincent Tu  and
Bernard Wong
Benjamin Avanzi
Affiliation:
School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW Sydney NSW 2052, Australia, Département de Mathématiques et de Statistique, Université de Montréal, Montréal QC H3T 1J4, Canada, E-Mail: [email protected]
Vincent Tu*
Affiliation:
School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW Sydney NSW 2052, Australia
Bernard Wong
Affiliation:
School of Risk and Actuarial Studies, UNSW Australia Business School, UNSW Sydney NSW 2052, Australia, E-Mail: [email protected]
*
E-Mail: [email protected]
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Abstract

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In the classical optimal dividends problem, dividend decisions are allowed to be made at any point in time — according to a continuous strategy. Depending on the surplus process that is considered and whether dividend payouts are bounded or not, optimal strategies are generally of a band, barrier or threshold type. In reality, while surpluses change continuously, dividends are generally paid on a periodic basis. Because of this, the actuarial literature has recently considered strategies where dividends are only allowed to be distributed at (random) discrete times — according to a periodic strategy.

In this paper, we focus on the Brownian risk model. In this context, the optimal continuous and periodic strategies have previously been shown (independently of one another) to be of barrier type. For the first time, we consider a model where both strategies are used. In such a hybrid strategy, decisions are allowed to be made either at any time (continuously), or periodically at a lower cost. This proves optimal in some cases. We also determine under which combination of parameters a pure continuous, pure periodic or hybrid (including both continuous and periodic dividend payments) barrier strategy is optimal. Interestingly, the hybrid strategy lies in-between periodic and continuous strategies, which provides some interesting insights. Results are illustrated.

Keywords

Brownian motionStochastic controlDividendsHybrid strategiesBarrier strategiesTransaction costs
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 3 , September 2016 , pp. 709 - 746
Copyright
Copyright © Astin Bulletin 2016 

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