Optimal Periodic Dividend Strategies for Spectrally Positive Lévy Risk Processes With Fixed Transaction Costs

33 Pages Posted: 10 Jan 2019 Last revised: 8 May 2019

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Hayden Lau

UNSW Australia Business School, School of Risk & Actuarial Studies

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: December 19, 2018

Abstract

We consider the general class of spectrally positive Lévy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends are paid periodically in real life, we study periodic dividend strategies whereby dividend decisions are made according to a Poisson arrival process.

In this paper, we investigate the impact of fixed transaction costs on the optimal periodic dividend strategy, and show that a periodic (b u , b l ) strategy is optimal. Such a strategy leads to lump sum dividends that bring the surplus back to b l as long as it is no less than b u at a dividend decision time. The expected present value of dividends (net of transaction costs) is provided explicitly with the help of scale functions. Results are illustrated.

Keywords: Optimal Dividends, Periodic Dividends, Dual Risk Model, Fixed Transaction Costs, SPLP

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

Suggested Citation

Avanzi, Benjamin and Lau, Hayden and Wong, Bernard, Optimal Periodic Dividend Strategies for Spectrally Positive Lévy Risk Processes With Fixed Transaction Costs (December 19, 2018). UNSW Business School Research Paper No. 2018ACTL02. Available at SSRN: https://ssrn.com/abstract=3303250 or http://dx.doi.org/10.2139/ssrn.3303250

Benjamin Avanzi

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

UNSW Sydney, NSW 2052
Australia

Hayden Lau (Contact Author)

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

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

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

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