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On the dual risk model with Parisian implementation delays under a mixed dividend strategy

Published online by Cambridge University Press:  09 January 2023

Kang Hu ,
Jingchao Li Open the ORCID record for Jingchao Li [Opens in a new window]  and
Jieming Zhou
Kang Hu
Affiliation:
MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P.R. China
Jingchao Li
Affiliation:
College of Mathematics and Statistics, Shenzhen University, Shenzhen, Guangdong 518060, P.R. China. E-mail: jingchaoli@szu.edu.cn
Jieming Zhou
Affiliation:
Key Laboratory of Applied Statistics and Data Science, Hunan Normal University, College of Hunan Province, Changsha, Hunan 410081, P.R. China. E-mail: jmzhou@hunnu.edu.cn
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Abstract

In this paper, we consider a mixed dividend strategy in a dual risk model. The mixed dividend strategy is the combination of a threshold dividend and a Parisian implementation delays dividend under periodic observation. Given a series of discrete observation points, when the surplus level is larger than the predetermined bonus barrier at observation point, the Parisian implementation delays dividend is immediately carried out, and the threshold dividend is performed continuously during the delayed period. We study the Gerber-Shiu expected discounted penalty function and the expected discounted dividend payments before ruin in such a dual risk model. Numerical illustrations are given to study the influence of relevant parameters on the ruin-related quantities and the selection of the optimal dividend barrier for a given initial surplus level.

Keywords

Dual risk modelExpected discounted dividendExpected discounted penalty functionParisian implementation delaysThreshold dividend
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Special Issue 2: Probability and stochastic modeling in actuarial science and related fields , April 2023 , pp. 442 - 461
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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