Dividends: From Refracting to Ratcheting

22 Pages Posted: 8 May 2018

See all articles by Hansjoerg Albrecher

Hansjoerg Albrecher

University of Lausanne; Swiss Finance Institute

Nicole Bäuerle

University of Karlsruhe

Martin Bladt

University of Lausanne

Date Written: April 26, 2018

Abstract

In this paper we consider an alternative dividend payment strategy in risk theory, where the dividend rate can never decrease. This addresses a concern that has often been raised in connection with the practical relevance of optimal classical dividend payment strategies of barrier and threshold type. We study the case where once during the lifetime of the risk process the dividend rate can be increased and derive corresponding formulae for the resulting expected discounted dividend payments until ruin. We first consider a general spectrally-negative Lévy risk model, and then re fine the analysis for a diffusion approximation and a compound Poisson risk model. It is shown that for the diffusion approximation the optimal barrier for the ratcheting strategy is characterized by an unexpected relation to the case of refracted dividend payments. Finally, numerical illustrations for the diffusion case indicate that with such a simple ratcheting dividend strategy the expected value of discounted dividends can already get quite close to the respective value of the refracted dividend strategy, the latter being known to be optimal among all admissible dividend strategies.

Keywords: optimal dividends, risk theory, Levy risk model, scale functions, diffusion

JEL Classification: G22, C61

Suggested Citation

Albrecher, Hansjoerg and Bäuerle, Nicole and Bladt, Martin, Dividends: From Refracting to Ratcheting (April 26, 2018). Swiss Finance Institute Research Paper No. 18-32. Available at SSRN: https://ssrn.com/abstract=3169185 or http://dx.doi.org/10.2139/ssrn.3169185

Hansjoerg Albrecher (Contact Author)

University of Lausanne ( email )

Quartier Chambronne
Lausanne, Vaud CH-1015
Switzerland

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Nicole Bäuerle

University of Karlsruhe ( email )

Postbox
D-76128 Karlsruhe, DE 76128
Germany

Martin Bladt

University of Lausanne ( email )

Quartier Chambronne
Lausanne, Vaud CH-1015
Switzerland

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