ON OPTIMAL DIVIDENDS IN THE DUAL MODEL

By Erhan Bayraktar, Andreas E. Kyprianou, Kazutoshi Yamazaki. ASTIN Bulletin: The Journal of the International Actuarial Association, 2012

141 citations recorded by the source corpus.

Abstract We revisit the dividend payment problem in the dual model of Avanzi et al. ([2–4]). Using the fluctuation theory of spectrally positive Lévy processes, we give a short exposition in which we show the optimality of barrier strategies for all such Lévy processes. Moreover, we characterize the optimal barrier using the functional inverse of a scale function. We also consider the capital injection problem of [4] and show that its value function has a very similar form to the one in which the horizon is the time of ruin.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/99ea9261474eefa96c54a647a0bedc725fc3009d

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Citations in the corpus

ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS (2013, background): “Recently, Bayraktar et al. (2013), using the fluctuation theory of spectrally positive Lévy processes, showed the optimality of barrier strategies for all such Lévy processes.”
Optimal dividends in the dual model under transaction costs (2013, unknown): “A series of numerical examples are provided to confirm the analytical results and to demonstrate the convergence to the no-transaction cost case, which was recently solved by Bayrakta et al. [8].”
Optimal dividends problem with a terminal value for spectrally positive Levy processes (2013, background): “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, methodology): “5 in Avanzi et al. (2014), we illustrate Lemma 3.6. In the view of the dividend frequency, the inequality γ γ+δ μ δ − 1 r0 > 0 can be rewritten as γ > γ0, where γ0 is the solution to γ0 γ0+δ μ δ − 1 r0(γ0) = 0. In a sense, larger rate of dividend results in higher barrier of dividend. From the persp”
Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs (2014, methodology): “In addition, one can see later that the method used in Bayraktar, Kyprianou and Yamazaki [11] cannot be applied to our model since their proof relies on certain characteristics of Lévy process.”