Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T20:04:19.726Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albrecher, H. & Thonhauser, S. (2009). Optimality results for dividend problems in insurance. RACSAM, 103(2), 295–320.CrossRefGoogle Scholar
Asmussen, S. & Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics, 20, 1–15.Google Scholar
Borodin, A.N. & Salminen, P. (1998). Handbook of Brownian Motion – Facts and Formulae. Birkhäuser Verlag, Basel.Google Scholar
Brigo, D. & Mercurio, F. (2006). Interest Rate Models – Theory and Practice, 2nd edition. Springer, Heidelberg.Google Scholar
Cont, R. & Tankov, P. (2004). Financial Modelling with Jump Processes. CRC Press, London.Google Scholar
Eisenberg, J. (2015). Optimal dividends under a stochastic interest rate. Insurance: Math. Econ, 65, 259–266.Google Scholar
Grandits, P., Hubalek, F., Schachermayer, W. & Zigo, M. (2007). Optimal expected exponential utility of dividend payments in Brownian risk model. Scandinavian Actuarial Journal, 2, 73–107.Google Scholar
Hubalek, F. & Schachermayer, W. (2004). Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE. Insurance: Mathematics and Economics, 34(2), 193–225.Google Scholar
Jacod, J. & Shiryaev, A. (2003). Limit Theorems for Stochastic Processes, 2nd edition. Springer, Berlin, Heidelberg.Google Scholar
Sato, K. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Edinburgh.Google Scholar
Schmidli, H. (2008). Stochastic Control in Insurance. Springer-Verlag, London.Google Scholar
Shreve, S.E., Lehoczky, J.P. & Gaver, D.P. (1984). Optimal consumption for general diffusions with absorbing and reflecting barriers. SIAM Journal on Control and Optimization , 22(1), 55–75.CrossRefGoogle Scholar