Optimal Dividends in the Dual Model with Diffusion

By Benjamin Avanzi, Hans U. Gerber. 2008

98 citations recorded by the source corpus.

In the dual model, the surplus of a company is a Levy process with sample paths that are skip-free downwards. In this paper, the aggregate gains process is the sum of a shifted compound Poisson process and an independent Wiener process. By means of Laplace transforms, it is shown how the expectation of the discounted dividends until ruin can be calculated, if a barrier strategy is applied, and how the optimal dividend barrier can be determined. Conditions for optimality are discussed and several numerical illustrations are given. Furthermore, a family of models is analysed where the individual gain amount distribution is rescaled and compensated by a change of the Poisson parameter.

Subfields: Demography, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d24542e7fc095eca414a31176db4e8febaff7c21

Citations in the corpus

Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs (2014, unknown): “3) is a natural extension of the dual model in Avanzi and Gerber [5] and Avanzi et al.”
ON OPTIMAL DIVIDENDS IN THE DUAL MODEL (2012, unknown): “KEYWORDS Dual model, dividends, capital injections, spectrally positive Lévy processes, scale functions.”
On a Periodic Dividend Barrier Strategy in the Dual Model with Continuous Monitoring of Solvency (2013, unknown): “(4.1) It is instructive to note that the above equation is equivalent to equation (3.4) in Avanzi et al. (2007).”
Optimal dividends problem with a terminal value for spectrally positive Levy processes (2013, unknown): “For example, Avanzi et al. (2007), Avanzi and Gerber (2008), Bayraktar and Egami (2008), Li and Wu (2009), Ng (2009), Yao, Yang and Wang (2010), Dai, Liu and Luan (2010, 2011), Avanzi, Shen and Wong (2011), Bayraktar, Kyprianou and Yamazaki (2013), Yin and Wen (2013) to name but a few.”
Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes (2017, unknown): “In Avanzi et al. (2007) and Avanzi and Gerber (2008), the authors studied how the expectation of the discounted dividends until ruin can be calculated in the dual compound Poisson risk model.”
Optimal dividends in the dual model under transaction costs (2013, unknown): “(2007), Bayraktar and Egami (2008), Avanzi and Gerber (2008), and Avanzi et al.”
Valuing equity-linked death benefits in jump diffusion models (2013, unknown): “See, for example, Täcklind (1942), Dufresne and Gerber (1988, 1989, 1991a, 1991b), Chan (1990), Gerber and Shiu (1998, 2005), Chan, Gerber and Shiu (2006), Gerber, Shiu and Smith (2006), Avanzi and Gerber (2008), and so on.”
ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS (2013, unknown): “Note that the dual model with diffusion in Avanzi and Gerber (2008) corresponds to the case in which (dx) = λF(dx), where λ > 0 is the Poisson parameter and F is the distribution of individual gains, and the rate of expenses is given by c0 = c + ∫ 1 0 x (dx).”