Hepatocellular carcinoma(HCC),which is essentially primary liver cancer,is closely related to CD8^(+)T cell immune infiltration and immune suppression.We constructed a CD8^(+)T cells related risk score model to predic...Hepatocellular carcinoma(HCC),which is essentially primary liver cancer,is closely related to CD8^(+)T cell immune infiltration and immune suppression.We constructed a CD8^(+)T cells related risk score model to predict the prognosis of HCC patients and provided therapeutic guidance based on the risk score.Using integrated bulk RNA sequencing(RNA-seq)and single-cell RNA sequencing(scRNA-seq)datasets,we identified stable CD8^(+)T cell signatures.Based on these signatures,a 3-gene risk score model,comprised of KLRB1,RGS 2,and TNFRSF1B was constructed.The risk score model was well validated through an independent external validation cohort.We divided patients into high-risk and low-risk groups according to the risk score and compared the differences in immune microenvironment between these two groups.Compared with low-risk patients,high-risk patients have higher M2-type macrophage content(P<0.0001)and lower CD8^(+)T cells infiltration(P<0.0001).High-risk patients predict worse response to immunotherapy treatment than low-risk patients(P<0.01).Drug sensitivity analysis shows that PI3K-β inhibitor AZD6482 and TGFβRII inhibitor SB505124 may be suitable therapies for high-risk patients,while the IGF-1R inhibitor BMS-754807 or the novel pyrimidine-based anti-tumor metabolic drug Gemcitabine could be potential therapeutic choices for low-risk patients.Moreover,expression of these 3-gene model was verified by immunohistochemistry.In summary,the establishment and validation of a CD8^(+)T cell-derived risk model can more accurately predict the prognosis of HCC patients and guide the construction of personalized treatment plans.展开更多
This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptoti...This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes.Further,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.展开更多
Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair...Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.展开更多
Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where cla...Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.展开更多
In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems ...In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems of integro-differential equations satisfied by the expected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov-dependent risk model without tax are established. The analytical solutions of the systems of integro-differential equations are also obtained by the iteration method.展开更多
In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duratio...In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.展开更多
This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with gi...This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.展开更多
In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compo...In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.展开更多
We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same wa...We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.展开更多
In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating acco...In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.展开更多
This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and F...This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.展开更多
Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be depende...Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.展开更多
In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning ...In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.展开更多
This study discusses the analysis of various modeling approaches such as genetic algorithms, fuzzy logic and evidential reasoning, and maintenance techniques applicable to the liquefied natural gas （LNG） carrier ope...This study discusses the analysis of various modeling approaches such as genetic algorithms, fuzzy logic and evidential reasoning, and maintenance techniques applicable to the liquefied natural gas （LNG） carrier operations in the maritime environment. The usefulness of these algorithms in the LNG carrier industry in the areas of risk assessment and maintenance modeling as a standalone or hybrid algorithm are identified. This is evidenced with illustrative case studies.展开更多
We study the severity of ruin in a Markov-dependent risk model in which the claim interarrivals and claim amounts are influenced by an external Markov chain. A system of integro-differential equation of the severity o...We study the severity of ruin in a Markov-dependent risk model in which the claim interarrivals and claim amounts are influenced by an external Markov chain. A system of integro-differential equation of the severity of ruin, given the initial environment state, is derived. Explicit formulas for the severity of ruin are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In the two state model, numerical illustration with exponential claim accounts are given.展开更多
Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of F...Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.展开更多
In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability fun...In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.展开更多
In this paper, we study the case of independent sums in multi-risk model. Assume that there exist k types of variables. The ith are denoted by （Xij,j ≥ 1）, which are i.i.d. with common density function fi（x） ∈ O...In this paper, we study the case of independent sums in multi-risk model. Assume that there exist k types of variables. The ith are denoted by （Xij,j ≥ 1）, which are i.i.d. with common density function fi（x） ∈ OR and finite mean, i =- 1,., k. We investigate local large deviations for partial sums ∑i=1^k Sni=∑i=1^k ∑j=1^ni Xij.展开更多
Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims fo...Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.展开更多
In this paper, we consider a general expression for Ф（u, x, y）, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. In the renewal risk model, this density...In this paper, we consider a general expression for Ф（u, x, y）, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is O. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for Ф（u, x, y）. Finally, we give a numerical example to illustrate the application of these results.展开更多
基金国家自然科学基金项目(No.81902513)山西省应用基础研究计划项目(No.202303021211114 and 202103021224228)山西省高等教育百亿工程“科技引导”专项(No.BYJL047)资助。
文摘Hepatocellular carcinoma(HCC),which is essentially primary liver cancer,is closely related to CD8^(+)T cell immune infiltration and immune suppression.We constructed a CD8^(+)T cells related risk score model to predict the prognosis of HCC patients and provided therapeutic guidance based on the risk score.Using integrated bulk RNA sequencing(RNA-seq)and single-cell RNA sequencing(scRNA-seq)datasets,we identified stable CD8^(+)T cell signatures.Based on these signatures,a 3-gene risk score model,comprised of KLRB1,RGS 2,and TNFRSF1B was constructed.The risk score model was well validated through an independent external validation cohort.We divided patients into high-risk and low-risk groups according to the risk score and compared the differences in immune microenvironment between these two groups.Compared with low-risk patients,high-risk patients have higher M2-type macrophage content(P<0.0001)and lower CD8^(+)T cells infiltration(P<0.0001).High-risk patients predict worse response to immunotherapy treatment than low-risk patients(P<0.01).Drug sensitivity analysis shows that PI3K-β inhibitor AZD6482 and TGFβRII inhibitor SB505124 may be suitable therapies for high-risk patients,while the IGF-1R inhibitor BMS-754807 or the novel pyrimidine-based anti-tumor metabolic drug Gemcitabine could be potential therapeutic choices for low-risk patients.Moreover,expression of these 3-gene model was verified by immunohistochemistry.In summary,the establishment and validation of a CD8^(+)T cell-derived risk model can more accurately predict the prognosis of HCC patients and guide the construction of personalized treatment plans.
基金Supported by the 333 High Level Talent Training Project of Jiangsu Provincethe National Natural Science Foundation of China(71871046)Science and Technology Projects of Sichuan Province(2021YFQ0007)。
文摘This paper considers the one-and two-dimensional risk models with a non-stationary claim-number process.Under the assumption that the claim-number process satisfies the large deviations principle,the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes.Further,as an application of the result of onedimensional risk model,we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.
基金Supported by the Natural Science Foundation of China(12071487,11671404)the Natural Science Foundation of Anhui Province(2208085MA06)+1 种基金the Provincial Natural Science Research Project of Anhui Colleges(KJ2021A0049,KJ2021A0060)Hunan Provincial Innovation Foundation for Postgraduate(CX20200146)。
文摘Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.
基金The National Natural Science Foundation of China(No.11001052,11171065,71171046)China Postdoctoral Science Foundation(No.2012M520964)+1 种基金the Natural Science Foundation of Jiangsu Province(No.BK20131339)the Qing Lan Project of Jiangsu Province
文摘Consider two dependent renewal risk models with constant interest rate. By using some methods in the risk theory, uniform asymptotics for finite-time ruin probability is derived in a non-compound risk model, where claim sizes are upper tail asymptotically independent random variables with dominatedly varying tails, claim inter-arrival times follow the widely lower orthant dependent structure, and the total amount of premiums is a nonnegative stochastic process. Based on the obtained result, using the method of analysis for the tail probability of random sums, a similar result in a more complex and reasonable compound risk model is also obtained, where individual claim sizes are specialized to be extended negatively dependent and accident inter-arrival times are still widely lower orthant dependent, and both the claim sizes and the claim number have dominatedly varying tails.
基金Supported by the National Natural Science Foundation of China(11401498)the Fundamental Research Funds for the Central Universities(WUT:2015IVA066)
文摘In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems of integro-differential equations satisfied by the expected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov-dependent risk model without tax are established. The analytical solutions of the systems of integro-differential equations are also obtained by the iteration method.
基金The NNSF (10671072) of China"Shu Guang" project (04SG27) of Shanghai Municipal Education CommissionShanghai Education Development Foundation
文摘In this paper, we examine further annuity-due risk model presented by Cai （Probability in the Engineering and Informational Sciences, 16（2002）, 309-324）. We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.
基金supported in part by Hubei Normal University Post-graduate Foundation(2007D59 and 2007D60)the Science and Technology foundation of Hubei(D20092207)the National Natural Science Foundation of China(10671149)
文摘This article considers a Markov-dependent risk model with a constant dividend barrier. A system of integro-differential equations with boundary conditions satisfied by the expected discounted penalty function, with given initial environment state, is derived and solved. Explicit formulas for the discounted penalty function are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In two state model, numerical illustrations with exponential claim amounts are given.
基金Supported by the Natural Science Foundation of China(10071019)
文摘In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.
基金Supported in part by the National Natural Science Foundation of China and the Ministry of Education of China
文摘We consider a continuous time risk model based on a two state Markov process, in which after an exponentially distributed time, the claim frequency changes to a different level and can change back again in the same way. We derive the Laplace transform for the first passage time to surplus zero from a given negative surplus and for the duration of negative surplus. Closed-form expressions are given in the case of exponential individual claim. Finally, numerical results are provided to show how to estimate the moments of duration of negative surplus.
基金supported by the National Natural Science Foundation of China(11101451)Ph.D.Programs Foundation of Ministry of Education of China(20110191110033)
文摘In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.
基金Supported by the Natural Science Foundation of the Education Department of Anhui Province(0505101)
文摘This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.
基金Supported by the National Natural Science Foundation of China(Nos.11571058&11301481)Humanities and Social Science Foundation of the Ministry of Education of China(No.17YJC910007)+1 种基金Zhejiang Provincial Natural Science Foundation of China(No.LY17A010004)Fundamental Research Funds for the Central Universities(No.DUT17LK31)
文摘Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.
文摘In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.
文摘This study discusses the analysis of various modeling approaches such as genetic algorithms, fuzzy logic and evidential reasoning, and maintenance techniques applicable to the liquefied natural gas （LNG） carrier operations in the maritime environment. The usefulness of these algorithms in the LNG carrier industry in the areas of risk assessment and maintenance modeling as a standalone or hybrid algorithm are identified. This is evidenced with illustrative case studies.
基金Supported by the National Natural Science Foundation of China (10671149)Hubei Normal University Post-Graduate Foundation (2007D59, 2007D60)
文摘We study the severity of ruin in a Markov-dependent risk model in which the claim interarrivals and claim amounts are influenced by an external Markov chain. A system of integro-differential equation of the severity of ruin, given the initial environment state, is derived. Explicit formulas for the severity of ruin are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In the two state model, numerical illustration with exponential claim accounts are given.
基金Supported by the National Natural Science Foundation of China (70273029)
文摘Let R（t）=u＋ct-∑ I=1^N（t） Xi,t≥0 be the renewal risk model, with Fx（x）being the distribution function of the claim amount X. Let ψ（u） be the ruin probability with initial surplus u. Under the condition of Fx（x） ∈ S^＊（γ）,y ≥ 0, by the geometric sum method, we derive the local asymptotic behavior for ψ（u,u ＋ z] for every 0 （ z （ oo, On one hand, the asymptotic behavior of ψ（u） can be derived from the result obtained. On the other hand, the result of this paper can be applied to the insurance risk management of an insurance company.
基金Supported in part by the National Natural Science Foundation of China, the Guangdong Natural Science Foundation (S2011010004511)the Fundamental Research Funds for the Central Universities of China (201120102020005)
文摘In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.
文摘In this paper, we study the case of independent sums in multi-risk model. Assume that there exist k types of variables. The ith are denoted by （Xij,j ≥ 1）, which are i.i.d. with common density function fi（x） ∈ OR and finite mean, i =- 1,., k. We investigate local large deviations for partial sums ∑i=1^k Sni=∑i=1^k ∑j=1^ni Xij.
基金Supported by the National Natural Science Foundation of China(70871104)the Planning Project of the National Educational Bureau of China(08JA630078)the Project of Key Research Base of Human and Social Sciences(Finance) for Colleges in Zhejiang Province(Grant No. of Academic Education of Zhejiang [2008]255)
文摘Under the assumption that the claim size is subexponentially distributed and the insurance surplus is totally invested in risky asset, a simple asymptotic relation of tail probability of discounted aggregate claims for renewal risk model within finite horizon is obtained. The result extends the corresponding conclusions of related references.
文摘In this paper, we consider a general expression for Ф（u, x, y）, the joint density function of the surplus prior to ruin and the deficit at ruin when the initial surplus is u. In the renewal risk model, this density function is expressed in terms of the corresponding density function when the initial surplus is O. In the compound Poisson risk process with phase-type claim size, we derive an explicit expression for Ф（u, x, y）. Finally, we give a numerical example to illustrate the application of these results.
