Omega model for a jump–diffusion process with a two-step premium rate

He, Jianjia; Gao, Zhongqin; Wang, Bingbing

doi:10.1016/j.jkss.2019.01.005

Cited by 2 publications

(2 citation statements)

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“…On the basis of Kou, Chi [30] studied the jump-diffusion model with investment return in which the claim distribution was phase-type. Furthermore, the jump-diffusion model applied to the risk asset process has been studied by Zhang and Liang [31], He et al [32] and Guo et al [33].…”

Section: The Modelmentioning

confidence: 99%

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Numerical Method for a Perturbed Risk Model with Proportional Investment

2022

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In this paper, we study the perturbed risk model with a threshold dividend strategy and proportional investment. The insurance companies are allowed to invest their surplus in a financial market consisting of a risk-free asset and a risky asset in fixed proportions; the risky assets are modeled by the jump-diffusion process. Firstly, using the theory of the stochastic process and stochastic analysis, we obtained the integro-differential equations satisfied by the expected discounted dividend payments and the discounted penalty function. Secondly, we obtained the numerical approximate solutions of the integro-differential equations through the sinc method, since the analytical solutions of them are not easy to obtain, and we found that the error is within a manageable range. Finally, we considered some numerical examples where the claim sizes follow an exponential distribution, a mixture of two exponential distributions or the lognormal distribution in detail, and explored how perturbations and proportional investment affect dividends and ruin probability. Moreover, sensitive analysis showed that the proportion of the risky investment, the diffusion coefficient, the distribution of the claims and the positive jump in the risky assets investment all have explicit impacts on dividends and ruin probability.

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Section: The Modelmentioning

confidence: 99%

“…R l denotes an approximate estimate of R(x l ), and δ(x) = ln x. By substituting the integral terms of ( 31) and (32) into Equation (30), substituting x with the sinc grid points x k (k = −q, −q + 1, . .…”

Section: Numerical Solutions Of the Expected Discounted Dividend Paym...mentioning

confidence: 99%