Equilibrium behavior of a stochastic system with secondary input

1971 ◽  
Vol 8 (02) ◽  
pp. 252-260 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Stochastic System ◽  
Queueing Theory ◽  
Risk Theory ◽  
Insurance Risk ◽  
Statistical Nature ◽  
Equilibrium Behavior ◽  
Continuous Output ◽  
Storage Theory

Summary Equilibrium behavior of a stochastic system with two types of input of different statistical nature and with linear continuous output is investigated. The results have applications in queueing theory, storage theory and insurance-risk theory.

Equilibrium behavior of a stochastic system with secondary input

1971 ◽  
Vol 8 (2) ◽  
pp. 252-260 ◽  
Author(s):  
İzzet Şahin
Keyword(s):  
Stochastic System ◽  
Queueing Theory ◽  
Risk Theory ◽  
Insurance Risk ◽  
Statistical Nature ◽  
Equilibrium Behavior ◽  
Continuous Output ◽  
Storage Theory

SummaryEquilibrium behavior of a stochastic system with two types of input of different statistical nature and with linear continuous output is investigated. The results have applications in queueing theory, storage theory and insurance-risk theory.

Some duality results for a class of multivariate semi-markov processes

1982 ◽  
Vol 19 (01) ◽  
pp. 90-98
Author(s):  
J. Janssen ◽  
J. M. Reinhard
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Processes ◽  
Queueing Theory ◽  
Random Variables ◽  
Classical Case ◽  
Risk Theory ◽  
Finite Markov Chain ◽  
Duality Results ◽  
Semi Markov Processes

The duality results well known for classical random walk and generalized by Janssen (1976) for (J-X) processes (or sequences of random variables defined on a finite Markov chain) are extended to a class of multivariate semi-Markov processes. Just as in the classical case, these duality results lead to connections between some models of risk theory and queueing theory.

Some asymptotic results for transient random walks with applications to insurance risk

2001 ◽  
Vol 38 (01) ◽  
pp. 108-121 ◽  
Author(s):  
Aleksandras Baltrūnas
Keyword(s):  
Random Walk ◽  
Ruin Probability ◽  
Risk Theory ◽  
Insurance Risk ◽  
Asymptotic Results ◽  
First Passage ◽  
Tail Behaviour ◽  
Heavy Tailed ◽  
Exact Rate Of Convergence ◽  
Passage Times

We consider a real-valued random walk which drifts to -∞ and is such that the step distribution is heavy tailed, say, subexponential. We investigate the asymptotic tail behaviour of the distribution of the upwards first passage times. As an application, we obtain the exact rate of convergence for the ruin probability in finite time. Our result supplements similar theorems in risk theory.

Some duality results for a class of multivariate semi-markov processes

1982 ◽  
Vol 19 (1) ◽  
pp. 90-98 ◽  
Author(s):  
J. Janssen ◽  
J. M. Reinhard
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Processes ◽  
Queueing Theory ◽  
Random Variables ◽  
Classical Case ◽  
Risk Theory ◽  
Finite Markov Chain ◽  
Duality Results ◽  
Semi Markov Processes

The duality results well known for classical random walk and generalized by Janssen (1976) for (J-X) processes (or sequences of random variables defined on a finite Markov chain) are extended to a class of multivariate semi-Markov processes. Just as in the classical case, these duality results lead to connections between some models of risk theory and queueing theory.

A decision theoretic formulation of insurance risk theory

1972 ◽  
Vol 1972 (2) ◽  
pp. 155-169
Author(s):  
Robert B. Miller
Keyword(s):  
Risk Theory ◽  
Insurance Risk

scholarly journals Some Transient Results on the M/SM/1 Special Semi-Markov Model in Risk and Queueing Theories

1980 ◽  
Vol 11 (1) ◽  
pp. 41-51 ◽  
Author(s):  
Jacques Janssen
Keyword(s):  
Explicit Expression ◽  
Queueing Theory ◽  
Time Distribution ◽  
Risk Theory ◽  
Arrival Process ◽  
Waiting Time Distribution ◽  
The Matrix ◽  
Semi Markov Process ◽  
Aggregate Claims ◽  
First Time

We consider a usual situation in risk theory for which the arrival process is a Poisson process and the claim process a positive (J — X) process inducing a semi-Markov process. The equivalent in queueing theory is the M/SM/1 model introduced for the first time by Neuts (1966).For both models, we give an explicit expression of the probability of non-ruin on [o, t] starting with u as initial reserve and of the waiting time distribution of the last customer arrived before t. “Explicit expression” means in terms of the matrix of the aggregate claims distributions.

Tail Asymptotics of the Supremum of a Regenerative Process

2007 ◽  
Vol 44 (02) ◽  
pp. 349-365
Author(s):  
Zbigniew Palmowski ◽  
Bert Zwart
Keyword(s):  
Queueing Theory ◽  
Heavy Tails ◽  
Regenerative Process ◽  
Tail Asymptotics ◽  
Asymptotic Estimates ◽  
Tail Behavior ◽  
Insurance Risk ◽  
Light Tails ◽  
Precise Asymptotic

We give precise asymptotic estimates of the tail behavior of the distribution of the supremum of a process with regenerative increments. Our results cover four qualitatively different regimes involving both light tails and heavy tails, and are illustrated with examples arising in queueing theory and insurance risk.

Some asymptotic results for transient random walks with applications to insurance risk

2001 ◽  
Vol 38 (1) ◽  
pp. 108-121 ◽  
Author(s):  
Aleksandras Baltrūnas
Keyword(s):  
Random Walk ◽  
Ruin Probability ◽  
Risk Theory ◽  
Insurance Risk ◽  
Asymptotic Results ◽  
First Passage ◽  
Tail Behaviour ◽  
Heavy Tailed ◽  
Exact Rate Of Convergence ◽  
Passage Times

We consider a real-valued random walk which drifts to -∞ and is such that the step distribution is heavy tailed, say, subexponential. We investigate the asymptotic tail behaviour of the distribution of the upwards first passage times. As an application, we obtain the exact rate of convergence for the ruin probability in finite time. Our result supplements similar theorems in risk theory.

scholarly journals Asymptotically Normal Estimators of the Gerber-Shiu Function in Classical Insurance Risk Model

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1638
Author(s):  
Wen Su ◽  
Wenguang Yu
Keyword(s):  
Asymptotic Normality ◽  
Nonparametric Estimation ◽  
Risk Model ◽  
Risk Theory ◽  
Insurance Risk ◽  
Asymptotically Normal ◽  
Laguerre Series ◽  
Claim Number ◽  
Novel Method ◽  
Insurance Risk Model

Nonparametric estimation of the Gerber-Shiu function is a popular topic in insurance risk theory. Zhang and Su (2018) proposed a novel method for estimating the Gerber-Shiu function in classical insurance risk model by Laguerre series expansion based on the claim number and claim sizes of sample. However, whether the estimators are asymptotically normal or not is unknown. In this paper, we give the details to verify the asymptotic normality of these estimators and present some simulation examples to support our result.

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