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On optimal dividends: From reflection to refraction
Journal article   Open access   Peer reviewed

On optimal dividends: From reflection to refraction

Hans U Gerber and Elias S.W Shiu
Journal of computational and applied mathematics, Vol.186(1), pp.4-22
2006
DOI: 10.1016/j.cam.2005.03.062
url
https://doi.org/10.1016/j.cam.2005.03.062View
Published (Version of record) Open Access

Abstract

The problem goes back to a paper that Bruno de Finetti presented to the International Congress of Actuaries in New York (1957). In a stock company that is involved in risky business, what is the optimal dividend strategy, that is, what is the strategy that maximizes the expectation of the discounted dividends (until possible ruin) to the shareholders? Jeanblanc-Picqué and Shiryaev [Russian Math. Surveys 20 (1995) 257–277] and Asmussen and Taksar [Insurance: Math. Econom. 20 (1997) 1–15] solved the problem by modeling the income process of the company by a Wiener process and imposing the condition of a bounded dividend rate. Here, we present some down-to-earth calculations in this context.
Dividend strategy Smooth pasting condition Threshold strategy Regime switching

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