# On a Periodic Dividend Barrier Strategy in the Dual Model with Continuous Monitoring of Solvency

26 Pages Posted: 16 Oct 2012 Last revised: 6 Jul 2015

See all articles by Benjamin Avanzi

## Benjamin Avanzi

UNSW Australia Business School, School of Risk and Actuarial Studies

## Eric Cheung

The University of Hong Kong - Department of Statistics & Actuarial Science

## Bernard Wong

UNSW Australia Business School, School of Risk & Actuarial Studies

## Jae-Kyung Woo

The University of Hong Kong - Department of Statistics & Actuarial Science

Date Written: October 15, 2012

### Abstract

We consider the dual model, which is appropriate for modelling the surplus of companies with deterministic expenses and stochastic gains, such as pharmaceutical, petroleum or commission-based companies. Dividend strategies for this model that can be found in the literature include the barrier strategy (e.g., Avanzi et al., 2007) and the threshold strategy (e.g., Cheung, 2008), where dividend decisions are made continuously. While in practice the financial position of a company is typically monitored frequently, dividend decisions are only made periodically along with the publication of its books. In this paper, we introduce a dividend barrier strategy whereby dividend decisions are made only periodically, but still allow ruin to occur at any time (as soon as the surplus is exhausted). This is in contrast to Albrecher et al. (2011), who introduced periodic dividend payments in the Cramér-Lundberg surplus model, albeit with periodic ruin opportunities as well.

Under the assumption that the time intervals between dividend decisions are Erlang distributed, we derive integro-differential equations for the Laplace transform of the time to ruin and the expected present value of dividends until ruin. These are then solved with the help of probabilistic arguments. We also provide a recursive algorithm to compute these quantities. Finally, some numerical studies are presented, which aim at illustrating how our assumptions about dividend payments and ruin occurrence compare with those of the classical barrier strategy.

Keywords: dual model, barrier strategy, erlangization, dividends, ruin

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

Suggested Citation

Avanzi, Benjamin and Cheung, Eric and Wong, Bernard and Woo, Jae-Kyung, On a Periodic Dividend Barrier Strategy in the Dual Model with Continuous Monitoring of Solvency (October 15, 2012). Insurance: Mathematics and Economics, Volume 52, Issue 1, January 2013, Pages 98–113. Available at SSRN: https://ssrn.com/abstract=2162251

Register