“Optimal Dividends: Analysis with Brownian Motion,” Ana C. Cebrián, Hans U. Gerber and Elias S.W. Shiu, January 2004

By Olivier Deprez. 2004

106 citations recorded by the source corpus.

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Some Optimal Dividends Problems (2004, methodology): “Gerber and Shiu (2004) consider this case for the Brownian motion risk model and show that the distribution of Du is a mixture of a degenerate distribution at 0 and an exponential distribution.”
On optimal dividends: From reflection to refraction (2006, unknown): “(iv) Following Deprez (2004), we note that, for X(0) = x and 0 < w < x ≤ b, V(x; b) = V(x – w; b – w) + L(x – w; b – w)V(w; b).”
Optimal dividend payments until ruin of diffusion processes when payments are subject to both fixed and proportional costs (2007, background): “The special case when X is a Brownian motion with drift, i.e. when µ and σ are constants, was dealt with in, for example, Asmussen and Taksar (1997), Gerber and Shiu (2004), and Jeanblanc-Picqué and Shiryaev (1995) (the latter also solved the case where d0 > 0).”
Distribution of the Present Value of Dividend Payments in a Lévy Risk Model (2007, methodology): “Discussion on ‘On optimal dividend strategies in the compound Poisson model’ (H. U. Gerber and E. S. W. Shiu).”
A Lévy Insurance Risk Process with Tax (2008, unknown): “2m σ 2 u − 1 , which recovers Equation (2.20) of [ 10 ].”