Dividend problem of an investment risk model under random observation

Chunwei Wang; Shaohua Li; Jiaen Xu; Shujing Wang; Chunwei Wang; Shaohua Li; Jiaen Xu; Shujing Wang

doi:10.3934/math.20241169

AIMS Mathematics

2024, Volume 9, Issue 9: 24039-24057. doi: 10.3934/math.20241169

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Dividend problem of an investment risk model under random observation

School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, Henan, China
^† These authors contributed equally to this work.

Received: 30 April 2024 Revised: 29 July 2024 Accepted: 08 August 2024 Published: 13 August 2024
MSC : 65C30, 91B05, 91G05

We mainly studied the dividend payout with a two-sided jumps risk model under random observation. The two-sided jumps in the model represent random claims and random returns. First, we obtained the integral differential equation of the expected dividend under the boundary conditions. Because the equations cannot be solved directly under normal circumstances, we chose the sinc numerical method here to approximate the solution of the equations. Then the error analysis of the approximate solution was carried out to illustrate the rationality of the numerical method. Finally, some concrete numerical examples were given.
- sinc numerical solution,
- discounted dividend payments,
- two-sided jumps,
- random observation
Citation: Chunwei Wang, Shaohua Li, Jiaen Xu, Shujing Wang. Dividend problem of an investment risk model under random observation[J]. AIMS Mathematics, 2024, 9(9): 24039-24057. doi: 10.3934/math.20241169

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Abstract

We mainly studied the dividend payout with a two-sided jumps risk model under random observation. The two-sided jumps in the model represent random claims and random returns. First, we obtained the integral differential equation of the expected dividend under the boundary conditions. Because the equations cannot be solved directly under normal circumstances, we chose the sinc numerical method here to approximate the solution of the equations. Then the error analysis of the approximate solution was carried out to illustrate the rationality of the numerical method. Finally, some concrete numerical examples were given.

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