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Research On Ruin Problems In Several Classes Risk Models

Posted on:2011-06-25Degree:DoctorType:Dissertation
Country:ChinaCandidate:J D LiaoFull Text:PDF
GTID:1119360305992822Subject:Probability theory and mathematical statistics
Abstract/Summary:PDF Full Text Request
Since many assumptions of classical risk models are not in according with actual situations in risk theory. It is of great significance to study the models much further.As matter of fact, some standing open problems still exist in the three basic risk models - the compound binomial risk model, the compound Poisson risk model and the renewal model. For example without adjustment coefficients, it is still devoteled to study ruin probability, distribution of the instant surplus before bankruptcy in the models. In addition, further inverstigations are also needed in these extended models, which are derived from classical risk models. This thesis aims to study futher the above problems.We first investigate the compound binomial risk models.On the basic of works about ruin probability, we study its explicit solutions.And as for heavy-tailed claims, we have derived its asymptotic solutions.Then the classical Poisson risk models are also considered with heavy-tailed claims and no adjustment coefficients. The asymptotic and local solutions of ruin probability are derived in the above assumptions.At last, it is studied further for the Poisson-Geometric risk model which was extended from classical Poisson risk models. The renewal equation which the Gerber-Shiu discounted penalty function satisfier is presented, and the explicit expression (Pollazek-Khinchin formula) of ruin probability is also obtained. Moreover, ruin probability is derived when the loss stochastic variable obeys the exponential distribution. Especially, the obtained result is consistent with that of the classical risk model under departure coefficient is zero.
Keywords/Search Tags:risk models, ruin probability, local solutions, renewal equations, the Pollazek-Khinchin formula
PDF Full Text Request
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