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A note on the optimal dividends paid in a foreign currency

Published online by Cambridge University Press:  10 November 2016

Julia Eisenberg  and
Paul Krühner Open the ORCID record for Paul Krühner [Opens in a new window]
Julia Eisenberg*
Affiliation:
Institute for Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstr. 8/E105-1, 1040 Vienna, Austria
Paul Krühner
Affiliation:
Institute for Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstr. 8/E105-1, 1040 Vienna, Austria
*
*Correspondence to: Julia Eisenberg, Institute for Statistics and Mathematical Methods in Economics, Vienna University of Technology. Tel: +43 (1) 58801-105177; E-mail: jeisenbe@fam.tuwien.ac.at
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Abstract

We consider an insurance entity endowed with an initial capital and a surplus process modelled as a Brownian motion with drift. It is assumed that the company seeks to maximise the cumulated value of expected discounted dividends, which are declared or paid in a foreign currency. The currency fluctuation is modelled as a Lévy process. We consider both cases: restricted and unrestricted dividend payments. It turns out that the value function and the optimal strategy can be calculated explicitly.

Keywords

Optimal controlHamilton–Jacobi–Bellman equationLévy processesDividendsForeign currency
Type
Papers
Information
Annals of Actuarial Science , Volume 11 , Issue 1 , March 2017 , pp. 67 - 73
Copyright
© Institute and Faculty of Actuaries 2016 

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