Abstract
In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber-Shiu function are obtained via martingale stopping.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L J Bo, R M Song, D Tang, Y J Wang, X W Yang. Lévy risk model with two-sided jumps and a barrier dividend strategy, Insurance Math Econom, 2012, 50: 280–291.
N Cai, S G Kou. Option pricing under a mixed-exponential jump diffusion model, Manage Sci, 2011, 57: 2067–2081.
B De Finetti. Su unimpostazione alternativa dell teoria collettiva del rischio, Transactions of the XVth International Congress of Actuaries, 1957, 2: 433–443.
H U Gerber. An extension of the renewal equation and its application in the collective theory of risk, Skandinavisk Aktuarietidskrift, 1970, 205–210.
H U Gerber, B Landry. On the discounted penalty at ruin in a jump-diffusion and the perpetual put option, Insurance Math Econom, 1998, 22: 263–276.
H U Gerber, E S W Shiu. On the time value of ruin, N Am Actuar J, 1998, 2: 48–72.
S G Kou, H Wang. First passage times of a jump diffusion process, Adv in Appl Probab, 2003, 35: 427–445.
C Labbéa, H S Sendov, K P Sendova. The Gerber-Shiu function and the generalized Cramér-Lundberg model, Appl Math Comput, 2011, 218: 3035–3056.
M R Pistorius. On exit and ergodicity of the spectrally one-sided Lévy process reflected at its infimum, J Theoret Probab, 2004, 17: 183–220.
K C Yuen, C C Yin. On optimality of the barrier strategy for a general Lévy risk process, Math Comput Modelling, 2011, 53: 1700–1707.
Z M Zhang, H Yang, S M Li. The perturbed compound Poisson risk model with two-sided jumps, J Comput Appl Math, 2010, 233: 1773–1784.
X W Zhou. On a classical risk model with a constant dividend barrier, N Am Actuar J, 2005, 9: 95–108.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the Natural Science Foundation of Jiangsu Province (BK20130260), the National Natural Science Foundation of China (11301369) and the Postdoctoral Science Foundation of China (2013M540371).
Rights and permissions
About this article
Cite this article
Dong, Yh., Chen, Y. & Zhu, Hf. Hyper-exponential jump-diffusion model under the barrier dividend strategy. Appl. Math. J. Chin. Univ. 30, 17–26 (2015). https://doi.org/10.1007/s11766-015-3211-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11766-015-3211-0