scholarly journals Uniform Estimate of the Finite-Time Ruin Probability for All Times in a Generalized Compound Renewal Risk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Qingwu Gao ◽  
Na Jin ◽  
Juan Zheng
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Uniform Estimate ◽  
Random Variables ◽  
Dependence Structure ◽  
Finite Time Ruin Probability ◽  
Renewal Risk Model ◽  
Renewal Risk ◽  
Compound Renewal Risk Model

We discuss the uniformly asymptotic estimate of the finite-time ruin probability for all times in a generalized compound renewal risk model, where the interarrival times of successive accidents and all the claim sizes caused by an accident are two sequences of random variables following a wide dependence structure. This wide dependence structure allows random variables to be either negatively dependent or positively dependent.

scholarly journals Ruin Probabilities and Deficit for the Renewal Risk Model with Phase-type Interarrival Times

2004 ◽  
Vol 34 (2) ◽  
pp. 315-332 ◽  
Author(s):  
F. Avram ◽  
M. Usábel
Keyword(s):  
Laplace Transform ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Theoretical Point ◽  
Finite Time Ruin Probability ◽  
Double Laplace Transform ◽  
Phase Type ◽  
Interarrival Times ◽  
Renewal Risk

This paper shows how the multivariate finite time ruin probability function, in a phase-type environment, inherits the phase-type structure and can be efficiently approximated with only one Laplace transform inversion.From a theoretical point of view, we also provide below a generalization of Thorin’s formula (1971) for the double Laplace transform of the finite time ruin probability, by considering also the deficit at ruin; the model is that of a Sparre Andersen (renewal) risk process with phase-type interarrival times.In the case when the claims distribution is of phase-type as well, we obtain also an alternative formula for the single Laplace transform in time (or “exponentially killed probability’’), in terms of the roots with positive real part of the Lundberg’s equations, which complements Asmussen’s representation (1992) in terms of the roots with negative real part.

scholarly journals Estimates for the Finite-Time Ruin Probability of a Time-Dependent Risk Model with a Brownian Perturbation

2020 ◽  
Vol 2020 ◽  
pp. 1-5 ◽  
Author(s):  
Kaiyong Wang ◽  
Yongfang Cui ◽  
Yanzhu Mao
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Time Dependent ◽  
Dependence Structure ◽  
Finite Time Ruin Probability ◽  
Dependent Model ◽  
Heavy Tailed ◽  
Time Dependent Model ◽  
Asymptotic Upper Bound

In this paper, we consider a time-dependent risk model with a Brownian perturbation. In this model, there is a dependence structure between the claim sizes and their corresponding interarrival times. Assuming the claim sizes have subexponential distributions, we obtain the asymptotic lower bound of the finite-time ruin probability. When the claim sizes have distributions from the class L∩D, the asymptotic upper bound of the finite-time ruin probability has been presented. These results confirm that when the claim sizes are heavy-tailed, the asymptotics of the finite-time ruin probability of this time-dependent model are insensitive to the Brownian perturbation.

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