On optimal dividends in the dual model
Abstract
We revisit the dividend payment problem in the dual model of Avanzi et al. ([2], [1], and [3]). 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 [3] and show that its value function has a very similar form to the one in which the horizon is the time of ruin.
 Publication:

arXiv eprints
 Pub Date:
 November 2012
 arXiv:
 arXiv:1211.7365
 Bibcode:
 2012arXiv1211.7365B
 Keywords:

 Mathematics  Probability;
 Quantitative Finance  Portfolio Management
 EPrint:
 To appear in the ASTIN Bulletin. Key words: dual model