Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Huang, Yubing; Li, Jing; Liu, Hengyu; Yu, Wenguang

doi:10.3390/math9090982

Cited by 4 publications

(3 citation statements)

References 27 publications

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“…Numerous scholars have analysed the mathematical probability model and explored the characteristic changes in bankruptcy models under diferent conditions [29][30][31]. In addition, several researchers have tried applying the ruin model to specifc insurance practices and have used mathematical methods to analyse insurance risks [32][33][34][35][36][37]. Insurance ruin theory-as the basic theory of insurance actuarial science, particularly insurance risk analysis-has broad applicability in actuarial practice.…”

Section: Literature Reviewmentioning

confidence: 99%

Research on a Model for an Empirical Analysis of Inherent Defect Insurance Based on Ruin Theory

Yan,

Chen,

Wang

et al. 2023

Discrete Dynamics in Nature and Society

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The system of inherent defect insurance is an important measure to serve the real economy through financial means and improve the quality of construction projects, which is the future development direction of China’s construction industry. However, the related research is not perfect due to the short implementation of the insurance. This could bring risks to the promotion of insurance for companies. Insurance ruin theory is an important method in risk management theory, so adopting it to manage the risk inherent defect insurance from the perspective of insurance companies is vital. The research starts with the classic insurance ruin theory and determines the coefficient of premium collection from the perspective of claim settlement distribution expectations. Furthermore, the approximate distribution of claim settlement is deduced, and a comprehensive risk assessment model is constructed. Finally, based on the data of insurance actuarial practice in Shanghai, both the ruin probability of inherent defect insurance in each insuring term and its average required initial reserve are calculated, which provides the analyses on the risks and main subitems of inherent defect insurance as well as relevant suggestions. Finally, the sensitivity analysis is used to further analyse the risk of different insurance stages of IDI, and the relevant measures are proposed. The research can provide theoretical assistances for insurance companies to carry out effective risk management and provide model tools to make scientific decisions.

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Section: Literature Reviewmentioning

confidence: 99%

Research on a Model for an Empirical Analysis of Inherent Defect Insurance Based on Ruin Theory

Yan,

Chen,

Wang

et al. 2023

Discrete Dynamics in Nature and Society

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“…Peng and Wang [6] discussed a compound risk model without diffusion in two different assets. Huang et al [21] considered the estimation of ruin probability in an insurance risk model with stochastic premium income. Zhu and Li [22] studied the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market.…”

Section: Literature Reviewmentioning

confidence: 99%

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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“…See, for example, Croux and Veraverbeke [1], Frees [2], Mnatsakanov et al [3], Pitts [4], Politis [5], and Veraverbeke [6]. In recent years, many nice results have been obtained by actuarial scholars, such as Huang et al [7], Li et al [8], You et al [9], Zhang and Yang [10], Zhang and Yang [11], Zhang [12], and Zhang and Yang [13]. As an extension of ruin probability, the Gerber-Shiu function has been introduced and studied for its statistical properties.…”

Section: Introductionmentioning

confidence: 99%

The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α-Stable Lévy Subordinator

Gao

You

2021

Mathematics

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In this paper, a nonparametric estimator of ruin probability is introduced in a spectrally negative Lévy process where the jump component is a tempered α-stable subordinator. Given a discrete record of high-frequency data, a threshold technique is proposed to estimate the mean of the jump size and use the Fourier transform and the Pollaczek–Khinchin formula to construct the estimator of ruin probability. The convergence rate of the integrated squared error for the estimator is studied.

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Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Cited by 4 publications

References 27 publications

Research on a Model for an Empirical Analysis of Inherent Defect Insurance Based on Ruin Theory

Research on a Model for an Empirical Analysis of Inherent Defect Insurance Based on Ruin Theory

Numerical Method for a Perturbed Risk Model with Proportional Investment

The Speed of Convergence of the Threshold Estimator of Ruin Probability under the Tempered α-Stable Lévy Subordinator

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