Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T03:01:03.927Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal barrier strategy for spectrally negative Lévy process discounted by a class of exponential Lévy processes

Published online by Cambridge University Press:  27 February 2018

Huanqun Jiang Open the ORCID record for Huanqun Jiang [Opens in a new window]
Huanqun Jiang*
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA
*
*Correspondence to: Huanqun Jiang, Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA. Tel: (541)737 4686. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we extend the optimality of the barrier strategy for the dividend payment problem to the setting that the underlying surplus process is a spectrally negative Lévy process and the discounting factor is an exponential Lévy process. The proof of the main result uses the fluctuation identities of spectrally negative Lévy processes. This extends recent results of Eisenberg for the case where the accumulated interest rate and surplus process are independent Brownian motions with drift.

Keywords

Optimal barrier strategySpectrally negative Lévy processFluctuation identitiesExponential Lévy process
Type
Paper
Information
Annals of Actuarial Science , Volume 12 , Issue 2 , September 2018 , pp. 326 - 337
Copyright
© Institute and Faculty of Actuaries 2018 

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

Akyildirim, E., Güney, I.E., Rochet, J.-C. & Soner, H.M. (2014). Optimal dividend policy with random interest rates. Journal of Mathematical Economics, 51, 93–101.Google Scholar
Asmussen, S. & Taksar, M. (1997). Controlled diffusion models for optimal dividend pay-out. Insurance: Mathematics and Economics, 20(1), 1–15.Google Scholar
Avanzi, B. (2009). Strategies for dividend distribution: a review. North American Actuarial Journal, 13(2), 217–251.Google Scholar
Avram, F., Kyprianou, A.E. & Pistorius, M.R. (2004). Exit problems for spectrally negative lévy processes and applications to (Canadized) Russian options. The Annals of Applied Probability, 14(1), 215–238.Google Scholar
Avram, F., Palmowski, Z. & Pistorius, M.R. (2007). On the optimal dividend problem for a spectrally negative lévy process. The Annals of Applied Probability, 17(1), 156–180.Google Scholar
Bayraktar, E., Kyprianou, A.E. & Yamazaki, K. (2013). On optimal dividends in the dual model. Astin Bulletin, 43(3), 359–372.Google Scholar
Bertoin, J. (1998). Lévy Processes, volume 121, Cambridge University Press, Cambridge.Google Scholar
De Finetti, B. (1957). Su unimpostazione alternativa della teoria collettiva del rischio. Transactions of the xvth International Congress of Actuaries, 2(1), 433–443.Google Scholar
Eisenberg, J. (2015). Optimal dividends under a stochastic interest rate. Insurance: Mathematics and Economics, 65, 259–266.Google Scholar
Eisenberg, J. & Krhner, P. (2017). A note on the optimal dividends paid in a foreign currency. Annals of Actuarial Science, 11(1), 67–73.Google Scholar
Gerber, H.U. & Shiu, E.S.W. (2006). On optimal dividend strategies in the compound Poisson model. North American Actuarial Journal, 10(2), 76–93.Google Scholar
Hipp, C. (2004). Stochastic control with application in insurance. In Stochastic Methods in Finance (pp. 127–164). Springer, Berlin Heidelberg.Google Scholar
Jiang, Z. & Pistorius, M.R. (2012). Optimal dividend distribution under Markov regime switching. Finance and Stochastics, 16(3), 449–476.Google Scholar
Kyprianou, A. (2006). Introductory Lectures on Fluctuations of Lévy Processes With Applications. Springer Science & Business Media, Berlin Heidelberg.Google Scholar
Loeffen, R.L. (2008). On optimality of the barrier strategy in de Finettis dividend problem for spectrally negative lévy processes. The Annals of Applied Probability, 18(5), 1669–1680.Google Scholar
Monique, J.-P. & Shiryaev, A.N. (1995). Optimization of the flow of dividends. Russian Mathematical Surveys, 50(2), 257–277.Google Scholar
Protter, P.E. (2005). Stochastic Integration and Differential Equations, Stochastic Modelling and Applied Probability. Springer, Berlin Heidelberg.Google Scholar
Revuz, D. & Yor, M. (2013). Continuous Martingales and Brownian Motion, volume 293, Springer Science & Business Media, Berlin Heidelberg GmbH, Berlin.Google Scholar
Sato, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge.Google Scholar
Schmidli, H. (2007). Stochastic Control in Insurance. Springer Science & Business Media, London.Google Scholar