共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, a jump–diffusion Omega model with a two-step premium rate is studied. In this model, the surplus process is a perturbation of a compound Poisson process by a Brown motion. Firstly, using the strong Markov property, the integro-differential equations for the Gerber–Shiu expected discounted penalty function and the bankruptcy probability are derived. Secondly, for a constant bankruptcy rate function, the renewal equations satisfied by the Gerber–Shiu expected discounted penalty function are obtained, and by iteration, the closed-form solutions of the function are also given. Further, the explicit solutions of the Gerber–Shiu expected discounted penalty function are obtained when the individual claim size is subject to exponential distribution. Finally, a numerical example is presented to illustrate some properties of the model. 相似文献
2.
In this paper, we consider an extension to the continuous time risk model for which the occurrence of the claim may be delayed and the time of delay for the claim is assumed to be random. Two types of dependent claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim. The time of occurrence of a by-claim is later than that of its associate main claim and the time of delay for the occurrence of a by-claim is random. An integro-differential equations system for the Gerber–Shiu discounted penalty function is established using the auxiliary risk models. Both the system of Laplace transforms of the Gerber–Shiu discounted penalty functions and the Gerber–Shiu discounted penalty functions with zero initial surplus are obtained. From Lagrange interpolating theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Exact representation for the solution of this equation is derived through an associated compound geometric distribution. Finally, examples are given with claim sizes that have exponential and a mixture of exponential distributions. 相似文献
3.
4.
In this paper, a compound Poisson risk model in the presence of a constant dividend barrier is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and and the time of delay for the claim is assumed to be random. A system of integro-differential equations with certain boundary conditions for the expected discounted penalty function is derived. We show that its solution can be expressed as the solution to the expected discounted penalty function in the same risk model with the absence of a barrier plus a linear combination of two linearly independent solutions to the associated homogeneous integro-differential equation. Using systems of integro-differential equations for the moment-generating function as well as for the arbitrary moments of the sum of discounted dividend payments until ruin, a matrix version of the dividends–penalty type relationship is derived. We also prove that ruin is certain under constant dividend barrier strategy. The closed form expressions are given when the claim amounts from both classes are exponentially distributed. Finally, a numerical example is presented to illustrate the solution procedure. 相似文献
5.
In this paper, we study the Gerber–Shiu (G-S) function for the classical risk model, in which the discount rate is generalized from a constant to a random variable. The discounted interest force accumulated process is modeled by a Poisson process and a Gaussian process for the G-S function. In terms of the standard techniques in ruin theory, we derive the integro-differential equation and the defective renewal equation satisfied by the G-S function. Then, the asymptotic formula for the G-S function is obtained using the renewal theory. 相似文献
6.
This article supposes that a large insurance company can control its surplus process by reinsurance, paying dividends, or injecting capitals. The exponential premium principle and proportional reinsurance are adopted in business activities. We investigate the general situation that the company needs to pay both proportional and fixed costs for dividends and capital injections. The object of the company is to determine an optimal joint reinsurance–dividend–capital injection strategy for maximizing the expected present value of dividends less capital injections until the time of bankruptcy. In both cases of non cheap and cheap reinsurance, we obtain the explicit solutions for value function and optimal strategy. 相似文献
7.
Jie-Hua Xie 《统计学通讯:理论与方法》2017,46(4):1898-1915
In this article, we consider a dependent risk model in the presence of a multi-laydividend strategy. We construct the dependence structure between the claim size and interclaim time by a Farlie–Gumbel–Morgenstern copula. A piecewise integro-differential equations for the expected discounted penalty function with boundary conditions are established. A renewal equation satisfied by the expected discounted penalty function is obtained via the translation operator. Then, we provide a recursive approach to derive the analytical solution of the expected discounted penalty function. Finally, a numerical example is presented to illustrate the solution procedure. 相似文献
8.
9.
We consider the compound Markov binomial risk model. The company controls the amount of dividends paid to the shareholders as well as the capital injections in order to maximize the cumulative expected discounted dividends minus the discounted capital injections and the discounted penalties for deficits prior to ruin. We show that the optimal value function is the unique solution of an HJB equation, and the optimal control strategy is a two-barriers strategy given the current state of the Markov chain. We obtain some properties of the optimal strategy and the optimal condition for ruining the company. We offer a high-efficiency algorithm for obtaining the optimal strategy and the optimal value function. In addition, we also discuss the optimal control problem under a restriction of bounded dividend rates. Numerical results are provided to illustrate the algorithm and the impact of the penalties. 相似文献
10.
随着计算机的飞速发展,极大地便利了数据的获取和存储,很多企业积累了大量的数据,同时数据的维度也越来越高,噪声变量越来越多,因此在建模分析时面临的重要问题之一就是从高维的变量中筛选出少数的重要变量。针对因变量取值为(0,1)区间的比例数据提出了正则化Beta回归,研究了在LASSO、SCAD和MCP三种惩罚方法下的极大似然估计及其渐进性质。统计模拟表明MCP的方法会优于SCAD和LASSO,并且随着样本量的增大,SCAD的方法也将优于LASSO。最后,将该方法应用到中国上市公司股息率的影响因素研究中。 相似文献
11.
This work investigates an optimal financing and dividend problem for an insurer whose surplus process is modulated by an observable continuous-time and finite-state Markov chain. We assume that the insurer should never go bankrupt by issuing new equity. The goal of the insurer is to maximize the expected present value of the dividends payout minus the discounted cost of equity issuance. We obtain the optimal policies and explicit expressions for the value functions when the risk reserve process is modeled by both upward jump model and its diffusion approximation. Numerical illustrations of the sensitivities of the model parameters are provided. 相似文献
12.
We consider the valuation problem of an (insurance) company under partial information. Therefore, we use the concept of maximizing discounted future dividend payments. The firm value process is described by a diffusion model with constant and observable volatility and constant but unknown drift parameter. For transforming the problem to a problem with complete information, we derive a suitable filter. The optimal value function is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation. We state a numerical procedure for approximating both the optimal dividend strategy and the corresponding value function. Furthermore, threshold strategies are discussed in some detail. Finally, we calculate the probability of ruin in the uncontrolled and controlled situation. 相似文献
13.
In this article, we provide a semiparametric approach to the joint measurement of technical and allocative inefficiency in a way that the internal consistency of the specification of allocative errors in the objective function (e.g., cost function) and the derivative equations (e.g., share or input demand functions) is assured. We start from the Cobb–Douglas production and shadow cost system. We show that the shadow cost system has a closed-form likelihood function contrary to what was previously thought. In turn, we use the method of local maximum likelihood applied to a system of equations to obtain firm-specific parameter estimates (which reveal heterogeneity in production) as well as measures of technical and allocative inefficiency and its cost. We illustrate its practical application using data on U.S. electric utilities. 相似文献
14.
15.
Jarkko Isotalo 《统计学通讯:理论与方法》2013,42(6):1011-1023
We consider the prediction of new observations in a general Gauss–Markov model. We state the fundamental equations of the best linear unbiased prediction, BLUP, and consider some properties of the BLUP. Particularly, we focus on such linear statistics, which preserve enough information for obtaining the BLUP of new observations as a linear function of them. We call such statistics linearly prediction sufficient for new observations, and introduce some equivalent characterizations for this new concept. 相似文献
16.
17.
从目前的现状看,我国上市公司与成熟资本市场相比存在现金分红普遍偏低的问题,运用股息收益率指标分析股票内在投资价值的策略在我国证券市场上还不是很广泛,这使市场的投机行为不能得到很好的控制。本文分析了股息收益率指标的优点,提出建立股息收益率为核心的股价评估体系,从而树立理性价值投资理念的可行性。 相似文献
18.
《Journal of Statistical Computation and Simulation》2012,82(9):1337-1342
Maximum-likelihood estimation technique is known to provide consistent and most efficient regression estimates but often this technique is tedious to implement, particularly in the modelling of correlated count responses. To overcome this limitation, researchers have developed semi- or quasi-likelihood functions that depend only on the correct specification of the mean and variance of the responses rather than on the distribution function. Moreover, quasi-likelihood estimation provides consistent and equally efficient estimates as the maximum-likelihood approach. Basically, the quasi-likelihood estimating function is a non-linear equation constituting of the gradient, Hessian and basic score matrices. Henceforth, to obtain estimates of the regression parameters, the quasi-likelihood equation is solved iteratively using the Newton–Raphson technique. However, the inverse of the Jacobian matrix involved in the Newton–Raphson method may not be easy to compute since the matrix is very close to singularity. In this paper, we consider the use of vector divisions in solving quasi-likelihood equations. The vector divisions are implemented to form secant method formulas. To assess the performance of the use of vector divisions with the secant method, we generate cross-sectional Poisson counts using different sets of mean parameters. We compute the estimates of the regression parameters using the Newton–Raphson technique and vector divisions and compare the number of non-convergent simulations under both algorithms. 相似文献
19.
Marginalised models, also known as marginally specified models, have recently become a popular tool for analysis of discrete longitudinal data. Despite being a novel statistical methodology, these models introduce complex constraint equations and model fitting algorithms. On the other hand, there is a lack of publicly available software to fit these models. In this paper, we propose a three-level marginalised model for analysis of multivariate longitudinal binary outcome. The implicit function theorem is introduced to approximately solve the marginal constraint equations explicitly. probit link enables direct solutions to the convolution equations. Parameters are estimated by maximum likelihood via a Fisher–Scoring algorithm. A simulation study is conducted to examine the finite-sample properties of the estimator. We illustrate the model with an application to the data set from the Iowa Youth and Families Project. The R package pnmtrem is prepared to fit the model. 相似文献
20.
Fangfang Bai Xuerong Chen Yan Chen Tao Huang 《Scandinavian Journal of Statistics》2019,46(4):1191-1205
The quantile residual lifetime function provides comprehensive quantitative measures for residual life, especially when the distribution of the latter is skewed or heavy‐tailed and/or when the data contain outliers. In this paper, we propose a general class of semiparametric quantile residual life models for length‐biased right‐censored data. We use the inverse probability weighted method to correct the bias due to length‐biased sampling and informative censoring. Two estimating equations corresponding to the quantile regressions are constructed in two separate steps to obtain an efficient estimator. Consistency and asymptotic normality of the estimator are established. The main difficulty in implementing our proposed method is that the estimating equations associated with the quantiles are nondifferentiable, and we apply the majorize–minimize algorithm and estimate the asymptotic covariance using an efficient resampling method. We use simulation studies to evaluate the proposed method and illustrate its application by a real‐data example. 相似文献