David Josafat Santana Cobian | Universidad Juárez Autónoma de Tabasco (original) (raw)
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Papers by David Josafat Santana Cobian
arXiv (Cornell University), Feb 10, 2023
Modern Stochastics: Theory and Applications
A new formula for the ultimate ruin probability in the Cramér–Lundberg risk process is provided w... more A new formula for the ultimate ruin probability in the Cramér–Lundberg risk process is provided when the claims are assumed to follow a finite mixture of m Erlang distributions. Using the theory of recurrence sequences, the method proposed here shifts the problem of finding the ruin probability to the study of an associated characteristic polynomial and its roots. The found formula is given by a finite sum of terms, one for each root of the polynomial, and allows for yet another approximation of the ruin probability. No constraints are assumed on the multiplicity of the roots and that is illustrated via a couple of numerical examples.
Communications in Statistics - Theory and Methods
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate th... more Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.
arXiv: Probability, 2020
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate th... more Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.
Methodology and Computing in Applied Probability, 2016
In this paper, we approximate the ultimate ruin probability in the Cramér-Lundberg risk model whe... more In this paper, we approximate the ultimate ruin probability in the Cramér-Lundberg risk model when claim sizes have an arbitrary continuous distribution. We propose two approximation methods, based on Erlang Mixtures, which can be used for claim sizes distribution both light and heavy tailed. Additionally, using a continuous version of the empirical distribution, we develop a third approximation which can be used when the claim sizes distribution is unknown and paves the way for a statistical application. Numerical examples for the gamma, Weibull and truncated Pareto distributions are provided.
Methodology and Computing in Applied Probability
arXiv (Cornell University), Feb 10, 2023
Modern Stochastics: Theory and Applications
A new formula for the ultimate ruin probability in the Cramér–Lundberg risk process is provided w... more A new formula for the ultimate ruin probability in the Cramér–Lundberg risk process is provided when the claims are assumed to follow a finite mixture of m Erlang distributions. Using the theory of recurrence sequences, the method proposed here shifts the problem of finding the ruin probability to the study of an associated characteristic polynomial and its roots. The found formula is given by a finite sum of terms, one for each root of the polynomial, and allows for yet another approximation of the ruin probability. No constraints are assumed on the multiplicity of the roots and that is illustrated via a couple of numerical examples.
Communications in Statistics - Theory and Methods
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate th... more Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.
arXiv: Probability, 2020
Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate th... more Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.
Methodology and Computing in Applied Probability, 2016
In this paper, we approximate the ultimate ruin probability in the Cramér-Lundberg risk model whe... more In this paper, we approximate the ultimate ruin probability in the Cramér-Lundberg risk model when claim sizes have an arbitrary continuous distribution. We propose two approximation methods, based on Erlang Mixtures, which can be used for claim sizes distribution both light and heavy tailed. Additionally, using a continuous version of the empirical distribution, we develop a third approximation which can be used when the claim sizes distribution is unknown and paves the way for a statistical application. Numerical examples for the gamma, Weibull and truncated Pareto distributions are provided.
Methodology and Computing in Applied Probability