A characterization for mixtures of semi-Markov processes

Mixtures of recurrent semi-Markov processes are characterized through a partial exchangeability condition of the array of successor states and holding times. A stronger invariance condition on the joint law of successor states and holding times leads to mixtures of Markov laws.     

方差分保费原则下相依多险种模型的最优再保险

采用共同冲击型相依多险种模型刻画保险公司的索赔风险过程,按照方差分保费原则计算再保险费,研究最小化破产概率的再保险问题.通过扩散逼近并利用动态规划原理,得到了显式最优策略和值函数.与采用期望值分保费原则比较,发现最优分保形式和自留风险水平均不相同;与最大化期望指数效用的结果比较,发现最优分保比例除了与安全负载相关,还与索赔分布、计数过程以及直接保险费收入率c有关.最后,结合数值算例揭示了相依参数的动态影响以及最优策略与c的敏感相关性.     

A basic formula for performance gradient estimation of semi-Markov decision processes

This paper presents a basic formula for performance gradient estimation of semi-Markov decision processes (SMDPs) under average-reward criterion. This formula directly follows from a sensitivity equation in perturbation analysis. With this formula, we develop three sample-path-based gradient estimation algorithms by using a single sample path. These algorithms naturally extend many gradient estimation algorithms for discrete-time Markov systems to continuous time semi-Markov models. In particular, they require less storage than the algorithm in the literature.     

Mean time to failure and availability of semi-Markov missions with maximal repair

We analyze mean time to failure and availability of semi-Markov missions that consist of phases with random sequence and durations. It is assumed that the system is a complex one with nonidentical components whose failure properties depend on the mission process. The stochastic structure of the mission is described by a Markov renewal process. We characterize mean time to failure and system availability under the maximal repair policy where the whole system is replaced by a brand new after successfully completing a phase before the next phase starts. Special cases involving Markovian missions are also considered to obtain explicit formulas.     

带干扰的一类相依风险模型

本文将古典风险模型推广为带干扰的一类相依风险模型。在此风险模型中,保单到达过程为一Pois-son过程,而索赔到达过程为保单到达过程的P-稀疏过程。利用鞅的方法得到了破产概率和Lundberg不等式。     

A semi-Markov maintenance model with credit rating application

Email: g.damico{at}unich.it Received on 6 December 2006. Accepted on 2 April 2008. The impact of a preventive rating maintenance policy on therating process is investigated through the definition of a semi-Markovmaintenance model with imperfect repair at random times. Theresults allow us to study the rating migrations process in thetransient and the asymptotic case.     

Finite non-homogeneous semi-Markov processes: Theoretical and computational aspects

This paper gives basic definitions and properties related to what we call the non-homogeneous semi-Markov processes with a finite number of states using the formalism of counting processes, i.e. with intensity functions. We show how it is possible to get generalized Polya processes as a very particular case. We also treat the computational aspect by discretisation and as an application, we develop a social security problem.     

Optimal risk probability for first passage models in semi-Markov decision processes

This paper studies the risk minimization problem in semi-Markov decision processes with denumerable states. The criterion to be optimized is the risk probability (or risk function) that a first passage time to some target set doesn't exceed a threshold value. We first characterize such risk functions and the corresponding optimal value function, and prove that the optimal value function satisfies the optimality equation by using a successive approximation technique. Then, we present some properties of optimal policies, and further give conditions for the existence of optimal policies. In addition, a value iteration algorithm and a policy improvement method for obtaining respectively the optimal value function and optimal policies are developed. Finally, two examples are given to illustrate the value iteration procedure and essential characterization of the risk function.     

Double-markov risk model

Given a new Double-Markov risk model DM=(μ,Q,ν,H;Y,Z) and Double-Markov risk process U={U(t),t≥ 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.     

A Scoring Criterion For Learning Chain Graphs

A chain graph allows both directed and undirected edges, and contains the underlying mathematical properties of the two. An important method of learning graphical models is to use scoring criteria to measure how well the graph structures fit the data. In this paper, we present a scoring criterion for learning chain graphs based on the Kullback Leibler distance. It is score equivalent, that is, equivalent chain graphs obtain the same score, so it can be used to perform model selection and model averaging.     

A time-series risk model with constant interest for dependent classes of business

In this paper, we propose a discrete-time model with dependent classes of business using a time-series approach. Specifically, premiums and claims of all classes are supposed to satisfy a multivariate first-order autoregressive time-series model. A constant interest rate is also included in the model. A Lundberg-type inequality for the ruin probability is deduced. We also give an example with constant premiums and two classes of claims for which an expression as well as an exponential bound for the ruin probability is given. A simulation study is provided to help understanding the model.     

Threshold dynamics and ergodicity of an SIRS epidemic model with semi-Markov switching

This work studies the threshold dynamics and ergodicity of a stochastic SIRS epidemic model with the disease transmission rate driven by a semi-Markov process. The semi-Markov process used in this paper for describing a randomly changing environment is a very large extension of the most common Markov regime-switching process. We define a basic reproduction number for the semi-Markov regime-switching environment and show that its position with respect to 1 determines the extinction or persistence of the disease. In the case of disease persistence, we give mild sufficient conditions for ensuring the existence and absolute continuity of the invariant probability measure. Under the same conditions, we also prove the global attractivity of the Ω-limit set of the system and the convergence in total variation norm of the transition probability to the invariant measure. Compared with the existing results in the Markov regime-switching environment, the results generalized require almost no additional conditions.     

On the Pyatetskii-Shapiro Criterion of Normality

In this paper, the Postnikov--Pyatetskii-Shapiro criterion of normality is given a more modern form. We obtain its unimprovable analogs for finite Markov chains, continued fractions, and generalized Bernoulli shifts.     

非平稳MDP--平均样本轨道最优

作者考虑的是任意状态空间,任意行动空间非平稳ＭＤＰ的平均样本轨道目标。在弱遍历条件下用鞅的极限理论,证明了最优马氏策略的存在性,推广了Ａ．Ａｒａｐｏｓｔａｔｈｉｓ,Ｖ．Ｂｏｒｋａｒ,Ｅ．Ｆ．Ｇａｕｃｈｅｒａｎｄ,Ｍ．Ｇｈｏｓｈ,Ｓ．Ｍａｒｃｕｓ（１９９３）的主要结果。     

二阶离散隐马尔科夫模型的严格定义及等价性质

隐马氏模型作为一种具有双重随机过程的统计模型,具有可靠的概率统计理论基础和强有力的数学结构,已被广泛应用于语音识别、生物序列分析、金融数据分析等领域.由于传统的一阶隐马氏模型无法表示更远状态距离间的依赖关系,就可能会忽略很多有用的统计特征,故有人提出二阶隐马氏模型的概念,但此概念并不严格.本文给出二阶离散隐马尔科夫模型的严格定义,并研究了二阶离散隐马尔科夫模型的两个等价性质.     

Ruin problems for an autoregressive risk model with dependent rates of interest

In this paper, we consider a discrete insurance risk model in which the claims, the premiums and the rates of interest are assumed to have dependent autoregressive structures (AR(1)). We derive recursive and integral equations for expected discounted penalty function. By these equations, we obtain generalized Lundberg inequality for the infinite time severity of ruin and hence for the infinite time ruin probability, consider asymptotic formula for the finite time ruin probability when loss distributions have regularly varying tails, and study some probability properties of the duration of ruin.     

马氏环境下的一类离散风险模型

文章主要讨论了马氏环境下的一类离散风险模型，其中在任意单位时间区间内的索赔情况由一三个状态的平稳马尔科夫链{Ik≥0）决定：Ik=0时，则第k个单位时间区间内没有索赔；Ik=1时，则发生一次X类索赔；Ik=2时，则发生一次Y类索赔．对此模型给出了条件破产概率的递推公式及某一特殊条件下的最终破产概率的上界．     

On Determination of the Order of a Markov Chain

In this paper we propose a new and more general criterion (the efficient determination criterion, EDC) for estimating the order of a Markov chain. The consistency and the strong consistency of the estimates have been established under mild conditions. This revised version was published online in August 2006 with corrections to the Cover Date.