On the Interface between Optimal Periodic and Continuous Dividend Strategies in the Presence of Transaction Costs

27 Pages Posted: 1 Apr 2015 Last revised: 19 May 2015

See all articles by Benjamin Avanzi

Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

Vincent Tu

UNSW Australia Business School, School of Risk & Actuarial Studies

Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

Date Written: April 3, 2015

Abstract

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. We analyse the interface between continuous and periodic strategies when transaction costs are introduced. In some cases, a hybrid strategy proves optimal. In such a strategy, decisions are allowed to be made either at any time (continuously), or periodically at a lower cost. We show under which combination of parameters a pure continuous, pure periodic or hybrid (including both continuous and periodic dividend payments) barrier strategy is optimal. Results are illustrated.

Keywords: Brownian motion, Stochastic control, Dividends, Hybrid strategies, Barrier strategies, Transaction costs

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

Suggested Citation

Avanzi, Benjamin and Tu, Vincent and Wong, Bernard, On the Interface between Optimal Periodic and Continuous Dividend Strategies in the Presence of Transaction Costs (April 3, 2015). UNSW Business School Research Paper No. 2015ACTL10. Available at SSRN: https://ssrn.com/abstract=2588037 or http://dx.doi.org/10.2139/ssrn.2588037

Benjamin Avanzi

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

UNSW Sydney, NSW 2052
Australia

Vincent Tu (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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