Optimal Dividends : Analysis with Brownian Motion

Details

Serval ID
serval:BIB_E12530D02CFE
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Optimal Dividends : Analysis with Brownian Motion
Journal
North American Actuarial Journal
Author(s)
Gerber H. U., Shiu E. S. W.
Publication state
Published
Issued date
2004
Peer-reviewed
Oui
Volume
8
Number
1
Pages
1-20
Language
english
Abstract
In the absence of dividends, the surplus of a company is modeled by a Wiener process (or Brownian motion) with positive drift. Now dividends are paid according to a barrier strategy: Whenever the (modified) surplus attains the level b, the ?overflow? is paid as dividends to shareholders. An explicit expression for the moment-generating function of the time of ruin is given. Let D denote the sum of the discounted dividends until ruin. Explicit expressions for the expectation and the moment-generating function of D are given; furthermore, the limiting distribution of D is determined when the variance parameter of the surplus process tends toward infinity. It is shown that the sum of the (undiscounted) dividends until ruin is a compound geometric random variable with exponentially distributed summands.
Create date
19/11/2007 11:51
Last modification date
20/08/2019 17:05
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