Parametric inference for ruin probability in the classical risk model

2018 ◽  
Vol 133 ◽  
pp. 28-37
Author(s):  
Takayoshi Oshime ◽  
Yasutaka Shimizu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Parametric Inference ◽  
Classical Risk Model ◽  
The Classical Risk Model

scholarly journals Nonparametric Estimation of the Ruin Probability in the Classical Compound Poisson Risk Model

2020 ◽  
Vol 13 (12) ◽  
pp. 298
Author(s):  
Yuan Gao ◽  
Lingju Chen ◽  
Jiancheng Jiang ◽  
Honglong You
Keyword(s):  
Nonparametric Estimation ◽  
Ruin Probability ◽  
Risk Model ◽  
Estimation Method ◽  
Asymptotic Distributions ◽  
Classical Risk Model ◽  
Compound Poisson Risk Model ◽  
The Fourier Transform ◽  
The Classical Risk Model ◽  
Asymptotic Variances

In this paper we study estimating ruin probability which is an important problem in insurance. Our work is developed upon the existing nonparametric estimation method for the ruin probability in the classical risk model, which employs the Fourier transform but requires smoothing on the density of the sizes of claims. We propose a nonparametric estimation approach which does not involve smoothing and thus is free of the bandwidth choice. Compared with the Fourier-transformation-based estimators, our estimators have simpler forms and thus are easier to calculate. We establish asymptotic distributions of our estimators, which allows us to consistently estimate the asymptotic variances of our estimators with the plug-in principle and enables interval estimates of the ruin probability.

scholarly journals Simulation of Ruin Probabilities for Subexponential Claims

1997 ◽  
Vol 27 (2) ◽  
pp. 297-318 ◽  
Author(s):  
S. Asmussen ◽  
K. Binswanger
Keyword(s):  
Ruin Probability ◽  
Asymptotic Efficiency ◽  
Risk Model ◽  
Ruin Probabilities ◽  
Simulation Methods ◽  
Classical Risk Model ◽  
Claim Size Distribution ◽  
Conditional Monte Carlo ◽  
Asymptotically Efficient ◽  
The Classical Risk Model

AbstractWe consider the classical risk model with subexponential claim size distribution. Three methods are presented to simulate the probability of ultimate ruin and we investigate their asymptotic efficiency. One, based upon a conditional Monte Carlo idea involving the order statistics, is shown to be asymptotically efficient in a certain sense. We use the simulation methods to study the accuracy of the standard Embrechts-Veraverbeke [16] approximation for the ruin probability and also suggest a new one based upon ideas of Hogan [21].

scholarly journals SIMPLE CONTINUITY INEQUALITIES FOR RUIN PROBABILITY IN THE CLASSICAL RISK MODEL-CORRIGENDUM

2016 ◽  
Vol 47 (1) ◽  
pp. 359-359
Author(s):  
Evgueni Gordienko ◽  
Patricia Vázquez-Ortega
Keyword(s):  
Markov Chains ◽  
Ruin Probability ◽  
Risk Model ◽  
Applied Probability ◽  
Classical Risk Model ◽  
The Classical Risk Model

In Gordienko and Vázquez-Ortega (2016) page 801, the following reference was listed incorrectly: Yu, M.A. (2005) Sensitivity and convergence of uniformly ergodic Markov chains. Journal of Applied Probabilities, 42, 1003–1014. It should have instead been listed as: Mitrophanov, A. Yu. (2005) Sensitivity and convergence of uniformly ergodic Markov chains. Journal of Applied Probability, 42, 1003–1014.We sincerely regret the error and any problems that have resulted for the authors and readers.

Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures

2016 ◽  
Vol 19 (3) ◽  
pp. 775-798 ◽  
Author(s):  
David J. Santana ◽  
Juan González-Hernández ◽  
Luis Rincón
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Classical Risk Model ◽  
The Classical Risk Model

scholarly journals On the Ruin Probability Under a Class of Risk Processes

2002 ◽  
Vol 32 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Wang Rongming ◽  
Liu Haifeng
Keyword(s):  
Laplace Transform ◽  
Renewal Process ◽  
Finite Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Claim Amount ◽  
Classical Risk Model ◽  
Finite Time Ruin Probability ◽  
Risk Processes ◽  
The Classical Risk Model

AbstractIn this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the finite time ruin probability is well given when the claim amount distribution is a mixed exponential. As its consequence, a well-known result about ultimate ruin probability in the classical risk model is obtained.

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