Optimal periodic dividend strategies for spectrally positive Lévy risk processes with fixed transaction costs

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ID: 282192
2020
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Abstract
We consider the general class of spectrally positive L\'evy risk processes, which are appropriate for businesses with continuous expenses and lump sum gains whose timing and sizes are stochastic. Motivated by the fact that dividends cannot be paid at any time in real life, we study $\textit{periodic}$ dividend strategies whereby dividend decisions are made according to a separate arrival process. In this paper, we investigate the impact of fixed transaction costs on the optimal periodic dividend strategy, and show that a periodic $(b_u,b_l)$ strategy is optimal when decision times arrive according to an independent Poisson process. Such a strategy leads to lump sum dividends that bring the surplus back to $b_l$ as long as it is no less than $b_u$ at a dividend decision time. The expected present value of dividends (net of transaction costs) is provided explicitly with the help of scale functions. Results are illustrated.
Reference Key
wong2020optimal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Benjamin Avanzi; Hayden Lau; Bernard Wong
Journal arXiv
Year 2020
DOI
DOI not found
URL
http://arxiv.org/abs/2003.13275v2
Keywords
math.oc math.pr q-fin.rm 60g51, 93e20, 91b30

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