On Optimal Joint Reflective and Refractive Dividend Strategies in Spectrally Positive Lévy Processes

28 Pages Posted: 7 Jul 2016

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

José-Luis Pérez

Centro de Investigacion en Matematicas (CIMAT) - Department of Probability and Statistics

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Kazutoshi Yamazaki

Kansai University - Department of Mathematics

Date Written: July 6, 2016

Abstract

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively.

In this paper, motivated by the behaviour of some dividend paying stock exchange companies, we determine the optimal dividend strategy when both continuous (refractive) and lump sum (reflective) dividends can be paid at any time, and if they are subject to different transaction rates.

We consider the general family of spectrally positive Lévy processes. Using scale functions, we obtain explicit formulas for the expected present value of dividends until ruin, with a penalty at ruin. We develop a verification lemma, and show that a two-layer $(a,b)$ strategy is optimal. Such a strategy pays continuous dividends when the surplus exceeds level $a>0$, and all of the excess over $b>a$ as lump sum dividend payments. Results are illustrated.

Keywords: Surplus models, Optimal dividends, Threshold strategy, Barrier strategy, Transaction costs

JEL Classification: C44, C61, G24, G32, G35

Suggested Citation

Avanzi, Benjamin and Pérez, José-Luis and Wong, Bernard and Yamazaki, Kazutoshi, On Optimal Joint Reflective and Refractive Dividend Strategies in Spectrally Positive Lévy Processes (July 6, 2016). UNSW Business School Research Paper No. 2016ACTL05. Available at SSRN: https://ssrn.com/abstract=2805454 or http://dx.doi.org/10.2139/ssrn.2805454

Benjamin Avanzi (Contact Author)

UNSW Australia Business School, School of Risk and Actuarial Studies ( email )

UNSW Sydney, NSW 2052
Australia

José-Luis Pérez

Centro de Investigacion en Matematicas (CIMAT) - Department of Probability and Statistics ( email )

Guanajuato
Mexico

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies ( email )

Room 2058 South Wing 2nd Floor
Quadrangle building, Kensington Campus
Sydney, NSW 2052
Australia

Kazutoshi Yamazaki

Kansai University - Department of Mathematics ( email )

3-3-35 Yamate-cho, Suita-shi
Osaka, 564-8680
Japan

HOME PAGE: http://https://sites.google.com/site/kyamazak/

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