This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is ...This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.展开更多
In this article, the expected discounted penalty function Фδ,α （u） with constant interest δ and ＂discounted factor＂ exp（-αTδ） is considered. As a result, the integral equation of Фδ,α （u） is derived a...In this article, the expected discounted penalty function Фδ,α （u） with constant interest δ and ＂discounted factor＂ exp（-αTδ） is considered. As a result, the integral equation of Фδ,α （u） is derived and an exact solution for Фδ,α （0） is found. The relation between the joint density of the surplus immediately prior to ruin, and the deficit at ruin and the density of the surplus immediately prior to ruin is then obtained based on analytical methods.展开更多
In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the stro...In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.展开更多
We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-...We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.展开更多
This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu...This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.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
We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk...We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.展开更多
In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then ge...In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.展开更多
In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically di...In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.展开更多
The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim ...The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.展开更多
In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus...In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.展开更多
In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as ...In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.展开更多
In this paper, we discuss the problem of extreme value for Brownian motion with positive drift. We obtain the joint distribution of the maximum excursion and the minimum excursion.
In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequ...In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.展开更多
Under constant interest force, the risk processes for old and new insurance business are modelled by Brownian motion with drift. By the stochastic control method, the explicit expressions for the minimum ruin probabil...Under constant interest force, the risk processes for old and new insurance business are modelled by Brownian motion with drift. By the stochastic control method, the explicit expressions for the minimum ruin probability and the corresponding optimal strategy are derived. Numerical example shows that the minimum probability of ruin and the optimal proportion for new business decrease as the interest rate increases, and vice versa.展开更多
The discrimination of synonyms has always been the key and difficult points in language learning.By using the British Na⁃tional Corpus(BNC)to retrieve the standard frequency,registers and collocations of the three com...The discrimination of synonyms has always been the key and difficult points in language learning.By using the British Na⁃tional Corpus(BNC)to retrieve the standard frequency,registers and collocations of the three common words,DESTORY,RUIN and DEMOLISH,this paper analyzes their similarities and differences.Besides,this paper demonstrates the strong ancillary func⁃tion of corpus in synonyms discrimination as well as in English teaching and learning.展开更多
Multimodal as digital literacies are,they have still been text-based.It has been a great concern that due to the popularity of speech-like writing style online,digital literacies have brought informal speech expressio...Multimodal as digital literacies are,they have still been text-based.It has been a great concern that due to the popularity of speech-like writing style online,digital literacies have brought informal speech expressions into formal standard writing,and thus increasing the possibility to ruin the standard writing language.On the other hand,although there are moral panics of the survival of standard written languages,scholars and popular media show great tolerance for online languages.In addition,it has been proved that some frequent participants in digital literacies nowadays are capable of both online language and standard offline language,indicating that they are well aware of the different registers of language use and therefore of high language literacy.Furthermore,researches suggest several possible merits of digital literacies,including saving young people from social isolation and depression,providing people with more opportunities to learn new things and to practice the instructional writing,calling for thorough consideration and elaborate editing and encouraging brief and clear writing style.展开更多
基金This work was supported in part by the National Natural Science Foundation of China (10071058, 70273029) the Ministry of Education of China.
文摘This article considers a risk model as in Yuen et al. （2002）. Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.
文摘In this article, the expected discounted penalty function Фδ,α （u） with constant interest δ and ＂discounted factor＂ exp（-αTδ） is considered. As a result, the integral equation of Фδ,α （u） is derived and an exact solution for Фδ,α （0） is found. The relation between the joint density of the surplus immediately prior to ruin, and the deficit at ruin and the density of the surplus immediately prior to ruin is then obtained based on analytical methods.
基金the National Natural Science Foundation of China(10571092)the major program of Key Research Institute of HumanitiesSocial Sciences at Universities(04JJD790006).
文摘In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.
文摘We consider that the reserve of an insurance company follows a renewal risk process with interest and dividend. For this risk process, we derive integral equations and exact infinite series expressions for the Cerber-Shiu discounted penalty function. Then we give lower and upper bounds for the ruin probability. Finally, we present exact expressions for the ruin probability in a special case of renewal risk processes.
基金supported by the Nature Science Foundation of Hebei Province(A2014202202)supported by the Nature Science Foundation of China(11471218)
文摘This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.
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 (10671149)the Ministry of Education of China, the Natural Science Foundation of Jiangxi(2008GQS0035)the Foundation of the Hubei Provincial Department of Education (B20091107)
文摘We consider a discrete time risk model in which the net payout （insurance risk） {Xk, k = 1, 2,...} are assumed to take real values and belong to the heavy-tailed class L∩ D and the discount factors （financial risk） {Yk, k = 1,2,...} concentrate on [θ, L], where 0 〈 0 〈 1, L 〈 ∞, {Xk, k = 1,2,...}, and {Yk, k=1,2,...} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n ≥ 1, which is different from Tang Q H and Tsitsiashvili G （Adv Appl Prob, 2004, 36： 1278-1299）.
基金Supported in part by the National Natural Science Foun-dation of China and the Ministry of Education of China
文摘In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given.
基金Research supported by National Science Foundation of China (70671018 and 10371117)
文摘In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.
文摘The classical risk process that is perturbed by diffusion is studied. The explicit expressions for the ruin probability and the surplus distribution of the risk process at the time of ruin are obtained when the claim amount distribution is a finite mixture of exponential distributions or a Gamma (2, α) distribution.
基金Supported by the National Natural Sci-ence Foundations of China (10271062 and 10471119)the Natural Science Foundation of Shandong Province(Y2004A06, Y2008A12, and ZR2009AL015)+1 种基金the Science Foundations of Shandong Provincial Education Department (J07yh05)the Science Foundations of Qufu Normal University (XJ0713, Bsqd200517)
文摘In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.
基金supported by National Ba-sic Research Program of China (973 Program, 2007CB814905)the Natural Science Foundation of China(10871102)
文摘In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved.
基金Supported by the National Natural Foundation of China(10271062,10411076)Supported by the Research Fund for the Doctorial Program of Qufu Normal University(20050701)
文摘In this paper, we discuss the problem of extreme value for Brownian motion with positive drift. We obtain the joint distribution of the maximum excursion and the minimum excursion.
基金Supported by the Grant to Supervisors of Postgraduates with Universities in Gansu Province(1001-10)
文摘In this note,one kind of insurance risk models with the policies having multiple validity times are investigated.Explicit expressions for the ruin probabilities are obtained by using the martingale method.As a consequence,the obtained probability serves as an upper bound for the ruin probability of a newly developed entrance processes based risk model.
基金The National Natural Science Foundations of China (No.10301011 and No.70271069)
文摘Under constant interest force, the risk processes for old and new insurance business are modelled by Brownian motion with drift. By the stochastic control method, the explicit expressions for the minimum ruin probability and the corresponding optimal strategy are derived. Numerical example shows that the minimum probability of ruin and the optimal proportion for new business decrease as the interest rate increases, and vice versa.
文摘The discrimination of synonyms has always been the key and difficult points in language learning.By using the British Na⁃tional Corpus(BNC)to retrieve the standard frequency,registers and collocations of the three common words,DESTORY,RUIN and DEMOLISH,this paper analyzes their similarities and differences.Besides,this paper demonstrates the strong ancillary func⁃tion of corpus in synonyms discrimination as well as in English teaching and learning.
文摘Multimodal as digital literacies are,they have still been text-based.It has been a great concern that due to the popularity of speech-like writing style online,digital literacies have brought informal speech expressions into formal standard writing,and thus increasing the possibility to ruin the standard writing language.On the other hand,although there are moral panics of the survival of standard written languages,scholars and popular media show great tolerance for online languages.In addition,it has been proved that some frequent participants in digital literacies nowadays are capable of both online language and standard offline language,indicating that they are well aware of the different registers of language use and therefore of high language literacy.Furthermore,researches suggest several possible merits of digital literacies,including saving young people from social isolation and depression,providing people with more opportunities to learn new things and to practice the instructional writing,calling for thorough consideration and elaborate editing and encouraging brief and clear writing style.
