An investment risk model with bilateral jumps

Chunwei Wang; Jiaen Xu; Shujing Wang; Naidan Deng; Chunwei Wang; Jiaen Xu; Shujing Wang; Naidan Deng

doi:10.3934/math.2024101

AIMS Mathematics

2024, Volume 9, Issue 1: 2032-2050. doi: 10.3934/math.2024101

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An investment risk model with bilateral jumps

Henan University of Science and Technology, Luoyang 471023, Henan Province, China
^† These authors contributed equally to this work

Received: 21 September 2023 Revised: 28 November 2023 Accepted: 11 December 2023 Published: 19 December 2023
MSC : 65C30, 91B05, 91G05

In this paper, an investment risk model with bilateral jumps was considered, assuming the insurer invested the surplus in two types of assets, namely, risk-free and risky ones, in a certain proportion. First, the integral-differential equations of the Gerber-Shiu function related to ruin and penalty were obtained, then, the sinc approximation method was used to obtain a numerical solution. Furthermore, we presented a special example for finding the explicit solutions (ES). By calculating the relative errors of the approximate solution (SA) and ES, we verified the superiority of the sinc method. Finally, several examples under different kinds of jumps were provided to show the impact of parameters such as investment ratio, discount factor or intensity of Poisson process on the ruin probability.
- Gerber-Shiu function,
- proportional investment,
- ruin probability,
- diffusion,
- sinc function
Citation: Chunwei Wang, Jiaen Xu, Shujing Wang, Naidan Deng. An investment risk model with bilateral jumps[J]. AIMS Mathematics, 2024, 9(1): 2032-2050. doi: 10.3934/math.2024101

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Abstract

In this paper, an investment risk model with bilateral jumps was considered, assuming the insurer invested the surplus in two types of assets, namely, risk-free and risky ones, in a certain proportion. First, the integral-differential equations of the Gerber-Shiu function related to ruin and penalty were obtained, then, the sinc approximation method was used to obtain a numerical solution. Furthermore, we presented a special example for finding the explicit solutions (ES). By calculating the relative errors of the approximate solution (SA) and ES, we verified the superiority of the sinc method. Finally, several examples under different kinds of jumps were provided to show the impact of parameters such as investment ratio, discount factor or intensity of Poisson process on the ruin probability.

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