Time to Turn Your Renewal Process Upside Down?

2022 ◽  
Vol 18 (2) ◽  
pp. 3-3
Keyword(s):  
Renewal Process

On some characterizations of the poisson process

1989 ◽  
Vol 26 (01) ◽  
pp. 176-181
Author(s):  
Wen-Jang Huang
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Arrival Time ◽  
Random Variables ◽  
Poisson Processes

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.

scholarly journals Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Renewal Process ◽  
Markov Chain Model ◽  
Markov Renewal Process ◽  
Renewal Processes ◽  
Chain Model ◽  
Markov Renewal Processes ◽  
Risky Bonds ◽  
Markov Structure

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.

Bayesian Analysis of a Superimposed Renewal Process

2010 ◽  
Vol 40 (2) ◽  
pp. 279-303 ◽  
Author(s):  
Chiranjit Mukhopadhyay ◽  
Mathews P. Samuel
Keyword(s):  
Bayesian Analysis ◽  
Renewal Process

scholarly journals Homogeneous Discrete Time Alternating Compound Renewal Process: A Disability Insurance Application

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Guglielmo D’Amico ◽  
Fulvio Gismondi ◽  
Jacques Janssen ◽  
Raimondo Manca
Keyword(s):  
Discrete Time ◽  
Renewal Process ◽  
Real Life ◽  
Disability Insurance ◽  
Insurance Contract ◽  
Compound Renewal Process ◽  
Simple Tool ◽  
Life Problems ◽  
Alternating Renewal Process

Discrete time alternating renewal process is a very simple tool that permits solving many real life problems. This paper, after the presentation of this tool, introduces the compound environment in the alternating process giving a systematization to this important tool. The claim costs for a temporary disability insurance contract are presented. The algorithm and an example of application are also provided.

Sign in / Sign up

Export Citation Format

Share Document