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About 1,191 papers for “Compound Poisson process”

Fuzzy Random Homogeneous Poisson Process and Compound Poisson Process

Shunqin Li, Ruiqing Zhao, Wansheng Tang · 2005

Abstract. By dealing with interarrival times as exponentially distributed fuzzy random variables, a fuzzy random homogeneous Poisson process and a fuzzy random compound Poisson process are respectively defined. Several theorems on the two processes are provided, respectively.

Cited by 2

Using a Compound Poisson Process

Jie Chen, Yu-ping Wang, Hong-wen Deng · 2010

permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To study chromosomal aberrations that may lead to cancer formation or genetic diseases, the array-based Comparative Genomic Hybridization (aCGH) technique is often used for detecting DNA copy number variants (CNVs). Various methods have been developed for gaining CNVs information based on aCGH data. However, most of these methods make use of the log-intensity ratios in aCGH data without taking advantage of other information such as the DNA probe (e.g., biomarker) positions/distances contained in the data. Motivated by the specific features of aCGH data, we developed a novel method that takes into account the estimation of a change point or locus of the CNV in aCGH data with its associated biomarker position on the chromosome using a compound Poisson process. We used a Bayesian approach to derive the posterior probability for the estimation of the CNV locus. To detect loci of multiple CNVs in the data, a sliding window process combined with our derived Bayesian posterior probability was proposed. To evaluate the performance of the method in the estimation of the CNV locus, we first performed simulation studies. Finally, we applied our approach to real data from aCGH experiments, demonstrating its applicability. 1.

Cited by 0

Confidence bounds for compound Poisson process

Marek Skarupski, Qinhao Wu · Statistical Papers · 2024

Abstract The compound Poisson process (CPP) is a common mathematical model for describing many phenomena in medicine, reliability theory and risk theory. However, in the case of low-frequency phenomena, we are often unable to collect a sufficiently large database to conduct analysis. In this article, we focused on methods for determining confidence intervals for the rate of the CPP when the sample size is small. Based on the properties of process parameter estimators, we proposed a new method for constructing such intervals and compared it with other known approaches. In numerical simulations, we used synthetic data from several continuous and discrete distributions. The case of CPP, in which rewards came from exponential distribution, was discussed separately. The recommendation of how to use each method to have a more precise confidence interval is given. All simulations were performed in R version 4.2.1.

Cited by 0Open access

Hedging in compound Poisson process model

Victor Sae Hon Sung · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2015

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cited by 0Open access

Hedging in compound Poisson process model

Victor Sae Hon Sung · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2015

Interessado em fazer com que o seu capital gere lucros, o investidor ao optar por negociar ativos, fica sujeito aos riscos econômicos de qualquer negociação, pois não existe uma certeza quanto a valorização ou desvalorização de um ativo. Eis que surge o mercado futuro, em que é possível negociar contratos a fim de se proteger (hedge) dos riscos de perdas ou ganhos excessivos, fazendo com que a compra ou venda de ativos, seja justa para ambas as partes. O objetivo deste trabalho consiste em estudar os processos de Lévy de puro salto de atividade finita, também conhecido como modelo de Poisson composto, e suas aplicações. Proposto pelo matemático francês Paul Pierre Lévy, os processos de Lévy tem como principal característica admitir saltos em sua trajetória, o que é frequentemente observado no mercado financeiro. Determinaremos uma estratégia de hedging no modelo de mercado com o processo de Poisson composto via o conceito de mean-variance hedging e princípio da programação dinâmica.

Cited by 0

Measuring Bayesian sensitivity in the compound Poisson process

Fabrizio Ruggeri, M. Sánchez-Sánchez, Alfonso Suárez‐Llorens · Test · 2025

Abstract Bayesian methods are widely used to determine insurance premiums, though they are sometimes criticized for the arbitrariness in selecting prior distributions. To mitigate this issue, classes of priors incorporating expert knowledge have been proposed, allowing for the analysis of uncertainty through upper and lower bounds on Bayesian premiums. In this paper, we employ a recently introduced class of priors based on stochastic orders, where the induced order on prior distributions is preserved in the corresponding posterior distributions. Uncertainty around a prior is captured through weighted functions, and the extremal elements of the class define premium bounds. We also show how dependence among parameters can be integrated using suitable weight functions. Our approach is developed within the framework of the compound Poisson process, a fundamental model for claim frequency and severity in car insurance. Additionally, we present a sensitivity analysis method for a bonus–malus system (BMS).

Cited by 0Open access

A Modified Compound Poisson Process with Normal Compounding

S. James Press · Journal of the American Statistical Association · 1968

The compound Poisson process in which the compounding variables are normally distributed is considered as a special case of a slightly more general process. The model is suggested for studying the behavior of security prices in the stock market. Distributional properties of the process are developed and it is shown that the distribution of the increments is skew-symmetric, peaked, “fat tailed,” and, generally, multimodal. A moment matching method based upon cumulants is suggested for estimating the parameters.

Cited by 21

A Stochastic String with a Compound Poisson Process

Sheng Fan · Abstract and Applied Analysis · 2013

We investigate a compound Poisson infinite factor diffusion model which describes the relationship between the infinite-dimension random risk resource and the corresponding stochastic process. We derive the no-arbitrage condition on the drift of instantaneous forward rates in the compound model and study the impact of random jump on the price of the zero-coupon bond.

Cited by 1Open access

On large deviations for compound mixed Poisson process

Aurelija Kasparavičiūtė, Dovilė Deltuvienė · Lietuvos matematikos rinkinys · 2013

This paper is designated for normal approximation to the distribution function of the compound mixed Poisson process taking into consideration large deviations both in the Cramér and power Linnik zones.

Cited by 0Open access

Property Claim Services by Compound Poisson Process And Inhomogeneous Levy Process

Muhammed A. S. Murad · Science Journal of University of Zakho · 2018

In this paper, stochastic compound Poisson process is employed to value the catastrophic insurance options and model the claim arrival process for catastrophic events, which were written in the loss period , during which the catastrophe took place. Here, a time compound process gives the underlying loss index before and after whose losses are revaluated by inhomogeneous exponential Levy process factor. For this paper, an exponential Levy process is used to evaluate the well-known European call option in order to price Property Claim Services catastrophe insurance based on catastrophe index.

Cited by 5Open access