Compound Compound Poisson Risk Model

2000 Mathematics Subject Classification: 60K10, 62P05.The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli risk model is discussed.This paper is partially supported by Sofia University grant 221/2008

A Modified Model of Risk Business

2000 Mathematics Subject Classification: 60K10, 62P05We consider the risk model in which the claim counting process {N(t)} is a modified stationary renewal process. {N(t)} is governed by a sequence of independent and identically distributed inter-occurrence times with a common exponential distribution function with mass at zero equal to ρ>0. The model is called a Polya-Aeppli risk model. The Cramer-Lundberg approximation and the martingale approach of the model are given.This paper is partially supported by Bulgarian NFSI grant MM-1103/2001

A Characterization of the Negative Binomial Distribution

Only a few characterizations have been obtained in literatute for the negative binomial distribution (see Johnson et al., Chap. 5, 1992). In this article a characterization of the negative binomial distribution related to random sums is obtained which is motivated by the geometric distribution characterization given by Khalil et al. (1991). An interpretation in terms of an unreliable system is given

On a Bivariate Poisson Negative Binomial Risk Process

In this paper we define a bivariate counting process as a compound Poisson process with bivariate negative binomial compounding distribution. We investigate some of its basic properties, recursion formulas and probability mass function. Then we consider a risk model in which the claim counting process is the defined bivariate Poisson negative binomial process. For the defined risk model we derive the distribution of the time to ruin in two cases and the corresponding Laplace transforms. We discuss in detail the particular case of exponentially distributed claims

Assessing bank's default probability using the ASRF model

In this paper it is shown how a Vasicek-model approach and the assumptions in Basel 2 regulatory framework can be used to develop measures of the probability of banks' failure. The Basel 2 framework is based on a Vasicek-model approach. The estimation of the propose measure of bank probability of default could be made over the capital ratio from supervisory authorities (non-public information) or over the capital ratio from balance sheet data (public available information)

The Pólya-Aeppli process and ruin problems

The Pólya-Aeppli process as a generalization of the homogeneous Poisson process is defined. We consider the risk model in which the counting process is the Pólya-Aeppli process. It is called a Pólya-Aeppli risk model. The problem of finding the ruin probability and the Cramér-Lundberg approximation is studied. The Cramér condition and the Lundberg exponent are defined. Finally, the comparison between the Pélya-Aeppli risk model and the corresponding classical risk model is given

Discrete Distributions Related to Success Runs of Length к in a Multi-State Markov Chain

[Kolev Nikolai; Колев Николай]; [Minkova Leda; Минкова Леда

A new Markov Binomial distribution

nrpages: 14status: publishe

A new Markov Binomial distribution

In this paper, we introduce a two state homogeneous Markov chain and define a geometric distribution related to this Markov chain. We define also the negative binomial distribution similar to the classical case and call it NB related to interrupted Markov chain. The new binomial distribution is related to the interrupted Markov chain. Some characterization properties of the Geometric distributions are given. Recursion formulas and probability mass functions for the NB distribution and the new binomial distribution are derived.Homogeneous Markov chain; Interrupted Markov chain; Geometric distribution related to Markov chain; In ated negative binomial distribution; New binomial distribution