An insurance risk process with a generalized income process: A solvency analysis

Wang, Zijia; Landriault, David; Li, Shu

doi:10.1016/j.insmatheco.2021.02.005

Cited by 5 publications

(4 citation statements)

References 23 publications

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“…However, an increasing number of scholars have been analysing insurance risk based on the insurance ruin model, which primarily analyses the accumulation of insurance companies' earnings over time [28]. 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].…”

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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“…In the Markov additive model (Section 2.3.4), the discount factor is allowed to be dependent on the state of the background Markov chain [75]. As an alternative to the classical exponential discounting as in (2.4), a version of discounting δ N t 1 is considered in [167] with respect to the number of claims N t for δ 1 ∈ (0, 1].…”

Section: Discount Factormentioning

confidence: 99%

“…After its first development [65] for the Cramér-Lundberg model (2.18), the Laplace transform based method has been employed, extended and improved in a wide variety of problem settings. Some examples include dependence between interclaim arrivals and claim sizes [24,124] together with perturbation [196], perturbation with two-sided jumps [198], perturbation and investment with penalty and reward in a finite time [17], delayed claims induced by main claims [177,207], random income modeled by a compound Poisson process [6] and additionally with delayed-claims [58,204], constant interests that can be positive or negative [139], capital injection restoring the surplus to a certain level [50], a finite-time problem with and without perturbation [106,107], and a generalized stochastic income with additional discounting [167]. Those studies succeed to obtain the the Laplace transform of the Gerber-Shiu function, or even the Gerber-Shiu function itself in explicit form by the inverse Laplace transform.…”

Section: Cramér-lundberg and Lévy Modelsmentioning

confidence: 99%

The Gerber-Shiu discounted penalty function: A review from practical perspectives

He¹,

Kawai²,

Shimizu³

et al. 2022

Preprint

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The Gerber-Shiu function provides a unified framework for the evaluation of a variety of risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas the conventional research has been focused on finding analytical or semi-analytical solutions, either of which is rarely available, except for limited classes of penalty functions on rather simple risk models. In contrast to its great generality, the Gerber-Shiu function does not seem sufficiently prevalent in practice, largely due to a variety of difficulties in numerical approximation and statistical inference. To enhance research activities on such implementation aspects, we provide a full review of existing formulations and underlying surplus processes, as well as an extensive survey of analytical, semi-analytical and asymptotic methods for the Gerber-Shiu function, which altogether shed fresh light on its numerical methods and statistical inference for further developments. On the basis of an exhaustive collection of 207 references, the present survey can serve as an insightful guidebook to model and method selection from practical perspectives as well.

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“…Recently, Su et al [ 22 ] provided a statistical method for estimating the Gerber–Shiu function; Ragulina [ 23 ] investigated the De Vylder approximation for the ruin probability and a constant dividend strategy in the risk model with stochastic premiums; and Dibu and Jacob [ 24 ] focused on a double barrier hybrid dividend strategy. Wang et al [ 25 ] quantitatively assessed the impact of the stochastic income process on some ruin quantities in detail.…”

Section: Introductionmentioning

confidence: 99%

Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random Variables

Guo

Wang

2023

Entropy

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In this paper, we propose a new discrete-time risk model of an insurance portfolio with stochastic premiums, in which the temporal dependence among the premium numbers of consecutive periods is fitted by the first-order integer-valued autoregressive (INAR(1)) process and the temporal dependence among the claim numbers of consecutive periods is described by the integer-valued moving average (INMA(1)) process. To measure the risk of the model quantitatively, we study the explicit expression for a function whose solution is defined as the Lundberg adjustment coefficient and give the Lundberg approximation formula for the infinite-time ruin probability. In the case of heavy-tailed claim sizes, we establish the asymptotic formula for the finite-time ruin probability via the large deviations of the aggregate claims. Two numerical examples are provided in order to illustrate our theoretical findings.

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An insurance risk process with a generalized income process: A solvency analysis

Cited by 5 publications

References 23 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

The Gerber-Shiu discounted penalty function: A review from practical perspectives

Ruin Analysis on a New Risk Model with Stochastic Premiums and Dependence Based on Time Series for Count Random Variables

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