Levy Risk Model with Two-Sided Jumps and a Barrier Dividend Strategy

28 Pages Posted: 11 Sep 2011 Last revised: 4 Feb 2014

See all articles by Xuewei Yang

Xuewei Yang

Nanjing University - School of Management and Engineering; Nanjing University - Institute of New Finance

Lijun Bo

University of Science and Technology of China (USTC)

Renming Song

affiliation not provided to SSRN

Dan Tang

affiliation not provided to SSRN

Yongjin Wang

Nankai University - Business School

Date Written: August 9, 2011

Abstract

In this paper, we consider a general Levy risk model with two-sided jumps and a constant dividend barrier. We connect the ruin problem of the ex-dividend risk process with the first passage problem of the Levy process reflected at its running maximum. We prove that if the positive jumps of the risk model form a compound Poisson process and the remaining part is a spectrally negative Levy process with unbounded variation, the Laplace transform (as a function of the initial surplus) of the upward entrance time of the reflected (at the running infimum) Levy process exhibits the smooth pasting property at the reflecting barrier. When the surplus process is described by a double exponential jump diffusion in the absence of dividend payment, we derive some explicit expressions for the Laplace transform of the ruin time, the distribution of the deficit at ruin, and the total expected discounted dividends. Numerical experiments concerning the optimal barrier strategy are performed and new empirical findings are presented.

Keywords: Risk model, Barrier strategy, Levy process, Two-sided jump, Time of ruin, Deficit, Expected discounted dividend, Optimal dividend barrier, Integro-differential operator, Double exponential distribution, Reflected jump-diffusions, Laplace transform

JEL Classification: G22, G33

Suggested Citation

Yang, Xuewei and Bo, Lijun and Song, Renming and Tang, Dan and Wang, Yongjin, Levy Risk Model with Two-Sided Jumps and a Barrier Dividend Strategy (August 9, 2011). Insurance: Mathematics and Economics, Vol. 50, No. 2, 2012, Available at SSRN: https://ssrn.com/abstract=1921934 or http://dx.doi.org/10.2139/ssrn.1921934

Xuewei Yang (Contact Author)

Nanjing University - School of Management and Engineering ( email )

22 Hankou Road, Gulou District
Nanjing, Jiangsu 210093
China

Nanjing University - Institute of New Finance ( email )

Nanjing, Jiangsu 210093
China

Lijun Bo

University of Science and Technology of China (USTC) ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China

Renming Song

affiliation not provided to SSRN ( email )

Dan Tang

affiliation not provided to SSRN ( email )

Yongjin Wang

Nankai University - Business School ( email )

94 Weijin Road, Nankai District
Tianjin, 300071
China

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