Inequalities for the ruin probability in a controlled discrete-time risk process

Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included

OPTIMAL POLICIES FOR DISCRETE TIME RISK PROCESSES WITH A MARKOV CHAIN INVESTMENT MODEL

We consider a discrete risk process modelled by a Markov Decision Process. The surplus could be invested in stock market assets. We adopt a realistic point of view and we let the investment return process to be statistically dependent over time. We assume that follows a Markov Chain model. To minimize the risk there is a possibility to reinsure a part or the whole reserve. We consider proportional reinsurance. Recursive and integral equations for the ruin probability are given. Generalized Lundberg inequalities for the ruin probabilities are derived. Stochastic optimal control theory is used to determine the optimal stationary policy which minimizes the ruin probability. To illustrate these results numerical examples are included.

Optimal policies for discrete time risk processes with a Markov chain investment model

We consider a discrete risk process modelled by a Markov Decision Process. The surplus could be invested in stock market assets. We adopt a realistic point of view and we let the investment return process to be statistically dependent over time. We assume that follows a Markov Chain model. To minimize the risk there is a possibility to reinsure a part or the whole reserve. We consider proportional reinsurance. Recursive and integral equations for the ruin probability are given. Generalized Lundberg inequalities for the ruin probabilities are derived. Stochastic optimal control theory is used to determine the optimal stationary policy which minimizes the ruin probability. To illustrate these results numerical examples are included

Inequalities for the ruin probability in a controlled discrete-time risk process

Ruin probabilities in a controlled discrete-time risk process with a Markov chain interest are studied. To reduce the risk there is a possibility to reinsure a part or the whole reserve. Recursive and integral equations for ruin probabilities are given. Generalized Lundberg inequalities for the ruin probabilities are derived given a constant stationary policy. The relationships between these inequalities are discussed. To illustrate these results some numerical examples are included.Risk process, Ruin probability, Proportional reinsurance, Lundberg`s

NWUC寿命分布类的一个充分条件

讨论 NWUC寿命分布类 ,证明了若一个更新过程的剩余寿命函数随时间依凸序随机递增 ,则其到达间隔是 NWUC的 .国家自然科学基金委员会数学天元基金 (TY 10 12 6 0 14);兰州大学博士启动基金资助项

Intergenerational Risk Sharing, Pensions and Endogenous Labor Supply in General Equilibrium

In the context of a two-tier pension system, with a pay-as-you-go first tier and a fully funded second tier, we demonstrate that a system with a defined wage-indexed second tier performs strictly better than one with a defined contribution or defined real benefit second tier. The former completely separates systematic redistribution (confined to the first tier) from intergenerational risk sharing (the role of the second tier). This way labor supply is undistorted.funded pensions, risk sharing, overlapping generations, endogenous labour supply

Determining potential 30/20 GHZ domestic satellite system concepts and establishment of a suitable experimental configuration

NASA is conducting a series of millimeter wave satellite communication systems and market studies to: (1) determine potential domestic 30/20 GHz satellite concepts and market potential, and (2) establish the requirements for a suitable technology verification payload which, although intended to be modest in capacity, would sufficiently demonstrate key technologies and experimentally address key operational issues. Preliminary results and critical issues of the current contracted effort are described. Also included is a description of a NASA-developed multibeam satellite payload configuration which may be representative of concepts utilized in a technology flight verification program

寿命分布年龄性质研究的总结与展望

本文对于寿命分布年龄性质过去20多年来的研究工作进行回顾,特别针对过去10年里我国寿命可靠性研究的工作结果加以总结。基于目前的研究现状我们也对未来的研究趋势和进一步发展做出展望。国家自然科学基金资助项目(11171278,11271356

Gerber-Shiu analysis in some dependent Sparre Andersen risk models

In this thesis, we consider a generalization of the classical Gerber-Shiu function in various risk models. The generalization involves introduction of two new variables in the original penalty function including the surplus prior to ruin and the deficit at ruin. These new variables are the minimum surplus level before ruin occurs and the surplus immediately after the second last claim before ruin occurs. Although these quantities can not be observed until ruin occurs, we can still identify their distributions in advance because they do not functionally depend on the time of ruin, but only depend on known quantities including the initial surplus allocated to the business. Therefore, some ruin related quantities obtained by incorporating four variables in the generalized Gerber-Shiu function can help our understanding of the analysis of the random walk and the resultant risk management. In Chapter 2, we demonstrate the generalized Gerber-Shiu functions satisfy the defective renewal equation in terms of the compound geometric distribution in the ordinary Sparre Andersen renewal risk models (continuous time). As a result, forms of joint and marginal distributions associated with the variables in the generalized penalty function are derived for an arbitrary distribution of interclaim/interarrival times. Because the identification of the compound geometric components is difficult without any specific conditions on the interclaim times, in Chapter 3 we consider the special case when the interclaim time distribution is from the Coxian class of distribution, as well as the classical compound Poisson models. Note that the analysis of the generalized Gerber-Shiu function involving three (the classical two variables and the surplus after the second last claim) is sufficient to study of four variable. It is shown to be true even in the cases where the interclaim of the first event is assumed to be different from the subsequent interclaims (i.e. delayed renewal risk models) in Chapter 4 or the counting (the number of claims) process is defined in the discrete time (i.e. discrete renewal risk models) in Chapter 5. In Chapter 6 the two-sided bounds for a renewal equation are studied. These results may be used in many cases related to the various ruin quantities from the generalized Gerber-Shiu function analyzed in previous chapters. Note that the larger number of iterations of computing the bound produces the closer result to the exact value. However, for the nonexponential bound the form of bound contains the convolution involving usually heavy-tailed distribution (e.g. heavy-tailed claims, extreme events), we need to find the alternative method to reinforce the convolution computation in this case