First hitting time of uncertain random renewal reward process and its application in insurance risk process

2018 ◽  
Vol 23 (11) ◽  
pp. 3687-3696 ◽  
Author(s):  
Kai Yao
Keyword(s):  
Risk Process ◽  
Hitting Time ◽  
First Hitting Time ◽  
Insurance Risk ◽  
Reward Process ◽  
Renewal Reward Process

scholarly journals An Uncertain Alternating Renewal Insurance Risk Model

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jia Zhai ◽  
Haitao Zheng ◽  
Manying Bai ◽  
Yunyun Jiang
Keyword(s):  
Risk Model ◽  
Risk Process ◽  
Insurance Risk ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Ruin Time ◽  
Reward Process ◽  
Renewal Reward Process ◽  
Explicit Expressions ◽  
Insurance Risk Model

The claim process in an insurance risk model with uncertainty is traditionally described by an uncertain renewal reward process. However, the claim process actually includes two processes, which are called the report process and the payment process, respectively. An alternative way is to describe the claim process by an uncertain alternating renewal reward process. Therefore, this paper proposes an insurance risk model under uncertain measure in which the claim process is supposed to be an alternating renewal reward process and the premium process is regarded as a renewal reward process. Then, the paper also gives the inverse uncertainty distribution of the insurance risk process. The expression of ruin index and the uncertainty distribution of the ruin time are derived which both have explicit expressions based on given uncertainty distributions. Finally, several examples are provided to illustrate the modeling ideas.

scholarly journals Randomization in the first hitting time problem

2009 ◽  
Vol 79 (23) ◽  
pp. 2422-2428 ◽  
Author(s):  
Ken Jackson ◽  
Alexander Kreinin ◽  
Wanhe Zhang
Keyword(s):  
Hitting Time ◽  
First Hitting Time ◽  
Time Problem

scholarly journals The density of a passage time for a renewal-reward process perturbed by a diffusion

2013 ◽  
Vol 26 (1) ◽  
pp. 108-112 ◽  
Author(s):  
Christophette Blanchet-Scalliet ◽  
Diana Dorobantu ◽  
Didier Rullière
Keyword(s):  
Passage Time ◽  
Reward Process ◽  
Renewal Reward Process

The Study on Convergence and Convergence Rate of Genetic Algorithm Based on an Absorbing Markov Chain

2012 ◽  
Vol 239-240 ◽  
pp. 1511-1515 ◽  
Author(s):  
Jing Jiang ◽  
Li Dong Meng ◽  
Xiu Mei Xu
Keyword(s):  
Genetic Algorithm ◽  
Markov Chain ◽  
Convergence Rate ◽  
Hitting Time ◽  
Sufficient Condition ◽  
First Hitting Time ◽  
Absorbing Markov Chain ◽  
Expected Hitting Time ◽  
Optimization Efficiency ◽  
Theoretical Issues

The study on convergence of GA is always one of the most important theoretical issues. This paper analyses the sufficient condition which guarantees the convergence of GA. Via analyzing the convergence rate of GA, the average computational complexity can be implied and the optimization efficiency of GA can be judged. This paper proposes the approach to calculating the first expected hitting time and analyzes the bounds of the first hitting time of concrete GA using the proposed approach.

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