scholarly journals FINITE TIME RUIN PROBABILITY IN MULTIVARIATE PERTURBED RENEWAL RISK MODEL

2022 ◽  
Vol 133 (2) ◽  
pp. 131-152
Author(s):  
Frédéric Béré
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Finite Time Ruin Probability ◽  
Renewal Risk Model ◽  
Renewal Risk

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.

Finite Time Ruin Probability of the Compound Renewal Model with Constant Interest Rate and Weakly Negatively Dependent Claims with Heavy Tails

2015 ◽  
Vol 17 (01) ◽  
pp. 1540011
Author(s):  
K. K. Thampi
Keyword(s):  
Finite Time ◽  
Ruin Probability ◽  
Heavy Tails ◽  
Risk Model ◽  
Finite Time Ruin Probability ◽  
Interest Force ◽  
Constant Interest Force ◽  
Renewal Risk ◽  
Constant Interest Rate ◽  
Constant Interest

This paper establishes a simple asymptotic formula for the finite time ruin probability of a compound renewal risk model with constant interest force. We assume that the claim sizes are Weakly Negatively Dependent (WND) and identically distributed random variables belonging to the class of regularly varying tails. The results obtained have extended and improved some corresponding results of related papers.

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